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Shrinkage estimation with singular priors and an application to small area estimation J. Multivar. Anal. (IF 1.136) Pub Date : 2021-01-19 Ryumei Nakada; Tatsuya Kubokawa; Malay Ghosh; Sayar Karmakar
The paper considers estimation of the multivariate normal mean under a multivariate normal prior with a singular precision matrix. Such a setup appears in the multi-task averaging, serial and spatial smoothing problems. The empirical and hierarchical Bayes estimators shrink the maximum likelihood estimator by projecting it to the null space of the precision matrix. Conditions for minimaxity are given
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Discussion about inaccuracy measure in information theory using co-copula and copula dual functions J. Multivar. Anal. (IF 1.136) Pub Date : 2021-01-14 Toktam Hosseini; Mehdi Jabbari Nooghabi
Inaccuracy measure is an important measure in information theory, which have been considered recently by many researchers, so that various generalizations have been introduced for this measure. In this paper, two new inaccuracy measures using co-copula and dual of a copula in copula theory are introduced and their properties under specific conditions are investigated. Including, under the establishment
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Estimating and forecasting dynamic correlation matrices: A nonlinear common factor approach J. Multivar. Anal. (IF 1.136) Pub Date : 2020-12-26 Yongli Zhang; Craig Rolling; Yuhong Yang
In economic and business data, the correlation matrix is a stochastic process that fluctuates over time and exhibits seasonality. The most widely-used approaches for estimating and forecasting the correlation matrix (e.g., multivariate GARCH) often are hindered by computational difficulties and require strong assumptions. In this paper we propose a method for modeling and forecasting correlation matrices
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Canonical correlation analysis for elliptical copulas J. Multivar. Anal. (IF 1.136) Pub Date : 2020-12-23 Benjamin W. Langworthy; Rebecca L. Stephens; John H. Gilmore; Jason P. Fine
Canonical correlation analysis (CCA) is a common method used to estimate the associations between two different sets of variables by maximizing the Pearson correlation between linear combinations of the two sets of variables. We propose a version of CCA for transelliptical distributions with an elliptical copula using pairwise Kendall’s tau to estimate a latent scatter matrix. Because Kendall’s tau
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Subspace rotations for high-dimensional outlier detection J. Multivar. Anal. (IF 1.136) Pub Date : 2020-12-29 Hee Cheol Chung; Jeongyoun Ahn
We propose a new two-stage procedure for detecting multiple outliers when the dimension of the data is much larger than the available sample size. In the first stage, the data are split into two disjoint sets, one containing non-outliers and the other containing the rest of the data that are considered as potential outliers. In the second stage, a series of hypothesis tests is conducted to test the
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Joint mean–covariance estimation via the horseshoe J. Multivar. Anal. (IF 1.136) Pub Date : 2020-12-29 Yunfan Li; Jyotishka Datta; Bruce A. Craig; Anindya Bhadra
Seemingly unrelated regression is a natural framework for regressing multiple correlated responses on multiple predictors. The model is very flexible, with multiple linear regression and covariance selection models being special cases. However, its practical deployment in genomic data analysis under a Bayesian framework is limited due to both statistical and computational challenges. The statistical
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Heterogeneous hypergeometric functions with two matrix arguments and the exact distribution of the largest eigenvalue of a singular beta-Wishart matrix J. Multivar. Anal. (IF 1.136) Pub Date : 2020-12-13 Koki Shimizu; Hiroki Hashiguchi
This paper discusses certain properties of heterogeneous hypergeometric functions with two matrix arguments. These functions are newly defined but have already appeared in statistical literature and are useful when dealing with the derivation of certain distributions for the eigenvalues of singular beta-Wishart matrices. The joint density function of the eigenvalues and the distribution of the largest
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Optimal designs for mixed continuous and binary responses with quantitative and qualitative factors J. Multivar. Anal. (IF 1.136) Pub Date : 2020-12-09 Ming-Hung Kao; Hazar Khogeer
This work is concerned with optimal designs for multivariate regression of responses of mixed variable types (continuous and binary) on quantitative and qualitative factors. New complete class results with respect to the Loewner ordering, and relevant Chebyshev systems are derived to identify a small class of designs, within which locally optimal designs can be found for a group of models and optimality
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Testing independence of functional variables by angle covariance J. Multivar. Anal. (IF 1.136) Pub Date : 2020-12-08 Tingyu Lai; Zhongzhan Zhang; Yafei Wang; Linglong Kong
We propose a new nonparametric independence test for two functional random variables. The test is based on a new dependence metric, the so-called angle covariance, which fully characterizes the independence of the random variables and generalizes the projection covariance proposed for random vectors. The angle covariance has a number of desirable properties, including the equivalence of its zero value
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Ordering results for elliptical distributions with applications to risk bounds J. Multivar. Anal. (IF 1.136) Pub Date : 2020-12-05 Jonathan Ansari; Ludger Rüschendorf
A classical result of Slepian (1962) for the normal distribution and extended by Das Guptas et al. (1972) for elliptical distributions gives one-sided (lower orthant) comparison criteria for the distributions with respect to the (generalized) correlations. Müller and Scarsini (2000) established that the ordering conditions even characterize the stronger supermodular ordering in the normal case. In
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On the specification of multivariate association measures and their behaviour with increasing dimension J. Multivar. Anal. (IF 1.136) Pub Date : 2020-11-23 Irène Gijbels; Vojtěch Kika; Marek Omelka
In this paper the interest is to elaborate on the generalization of bivariate association measures, namely Spearman’s rho, Kendall’s tau, Blomqvist’s beta and Gini’s gamma, for a general dimension d≥2. Desirable properties and axioms for such generalizations are discussed, where special attention is given to the impact of the addition of: (i) an independent random variable to a random vector; (ii)
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Dynamic tilted current correlation for high dimensional variable screening J. Multivar. Anal. (IF 1.136) Pub Date : 2020-11-04 Bangxin Zhao; Xin Liu; Wenqing He; Grace Y. Yi
Variable screening is a commonly used procedure in high dimensional data analysis to reduce dimensionality and ensure the applicability of available statistical methods. Such a procedure is complicated and computationally burdensome because spurious correlations commonly exist among predictor variables, while important predictor variables may not have large marginal correlations with the response variable
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On the copula correlation ratio and its generalization J. Multivar. Anal. (IF 1.136) Pub Date : 2020-11-26 Jia-Han Shih; Takeshi Emura
The correlation ratio has been used to measure how much the behavior of one variable can be predicted by the other variable. In this paper, we derive a new expression of the correlation ratio based on copulas. We represent the copula correlation ratio in terms of Spearman’s rho of the ∗-product of two copulas. Our expression provides a new way to obtain the copula correlation ratio, which is especially
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On the behavior of the DFA and DCCA in trend-stationary processes J. Multivar. Anal. (IF 1.136) Pub Date : 2020-11-17 Taiane Schaedler Prass; Guilherme Pumi
In this work, we develop the asymptotic theory of the Detrended Fluctuation Analysis (DFA) and Detrended Cross-Correlation Analysis (DCCA) for trend-stationary stochastic processes without any assumption on the specific form of the underlying distribution. All results are presented and derived under the general framework of potentially overlapping boxes for the polynomial fit. We prove the stationarity
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Approximating smooth functions by deep neural networks with sigmoid activation function J. Multivar. Anal. (IF 1.136) Pub Date : 2020-11-10 Sophie Langer
We study the power of deep neural networks (DNNs) with sigmoid activation function. Recently, it was shown that DNNs approximate any d-dimensional, smooth function on a compact set with a rate of order W−p∕d, where W is the number of nonzero weights in the network and p is the smoothness of the function. Unfortunately, these rates only hold for a special class of sparsely connected DNNs. We ask ourselves
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Analysis of the rate of convergence of fully connected deep neural network regression estimates with smooth activation function J. Multivar. Anal. (IF 1.136) Pub Date : 2020-11-10 Sophie Langer
This article contributes to the current statistical theory of deep neural networks (DNNs). It was shown that DNNs are able to circumvent the so-called curse of dimensionality in case that suitable restrictions on the structure of the regression function hold. In most of those results the tuning parameter is the sparsity of the network, which describes the number of non-zero weights in the network.
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Widening the scope of an eigenvector stochastic approximation process and application to streaming PCA and related methods J. Multivar. Anal. (IF 1.136) Pub Date : 2020-11-11 Jean-Marie Monnez; Abderrahman Skiredj
We prove the almost sure convergence of Oja-type processes to eigenvectors of the expectation B of a random matrix while relaxing the i.i.d. assumption on the observed random matrices (Bn) and assuming either (Bn) converges to B or (E[Bn|Tn]) converges to B where Tn is the sigma-field generated by the events before time n. As an application of this generalization, the online PCA of a random vector
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Testing multivariate quantile by empirical likelihood J. Multivar. Anal. (IF 1.136) Pub Date : 2020-11-20 Xuejun Ma; Shaochen Wang; Wang Zhou
In this paper, a new method called mean-of-quantile is introduced to estimate multivariate quantiles. The consistency and asymptotic normality of mean-of-quantile estimators are investigated. Furthermore, we apply empirical likelihood to mean-of-quantile estimators. The effectiveness of our new method is illustrated by Monte Carlo simulations and an empirical example.
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Kernel density estimation on symmetric spaces of non-compact type J. Multivar. Anal. (IF 1.136) Pub Date : 2020-09-09 Dena Marie Asta
We construct a kernel density estimator on symmetric spaces of non-compact type and establish an upper bound for its convergence rate, analogous to the minimax rate for classical kernel density estimators on Euclidean space. Symmetric spaces of non-compact type include hyperboloids of constant curvature −1 and spaces of symmetric positive definite matrices. This paper obtains a simplified formula in
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Sampling properties of color Independent Component Analysis J. Multivar. Anal. (IF 1.136) Pub Date : 2020-10-22 Seonjoo Lee; Haipeng Shen; Young Truong
Independent Component Analysis (ICA) offers an effective data-driven approach for blind source extraction encountered in many signal and image processing problems. Although many ICA methods have been developed, they have received relatively little attention in the statistics literature, especially in terms of rigorous theoretical investigation for statistical inference. The current paper aims at narrowing
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Non-asymptotic error controlled sparse high dimensional precision matrix estimation J. Multivar. Anal. (IF 1.136) Pub Date : 2020-10-03 Adam B. Kashlak
Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose a novel methodology for estimating such matrices while controlling the false positive rate, percentage of matrix entries incorrectly chosen to be non-zero. We specifically
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On the estimation of entropy in the FastICA algorithm J. Multivar. Anal. (IF 1.136) Pub Date : 2020-10-09 Elena Issoglio; Paul Smith; Jochen Voss
The fastICA method is a popular dimension reduction technique used to reveal patterns in data. Here we show both theoretically and in practice that the approximations used in fastICA can result in patterns not being successfully recognised. We demonstrate this problem using a two-dimensional example where a clear structure is immediately visible to the naked eye, but where the projection chosen by
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Multiply robust subgroup identification for longitudinal data with dropouts via median regression J. Multivar. Anal. (IF 1.136) Pub Date : 2020-10-07 Wenqi Lu; Guoyou Qin; Zhongyi Zhu; Dongsheng Tu
Subgroup identification serves as an important step towards precision medicine which has attracted great attention recently. On the other hand, longitudinal data with dropouts often arises in medical research. However there is little work in subgroup identification considering this data type. Therefore, in this paper we propose a new subgroup identification method based on concave fusion penalization
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Splitting models for multivariate count data J. Multivar. Anal. (IF 1.136) Pub Date : 2020-09-28 Jean Peyhardi; Pierre Fernique; Jean-Baptiste Durand
We investigate the class of splitting distributions as the composition of a singular multivariate distribution and a univariate distribution. It will be shown that most common parametric count distributions (multinomial, negative multinomial, multivariate hypergeometric, multivariate negative hypergeometric, …) can be written as splitting distributions with separate parameters for both components,
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Family of mean-mixtures of multivariate normal distributions: Properties, inference and assessment of multivariate skewness J. Multivar. Anal. (IF 1.136) Pub Date : 2020-09-25 Me’raj Abdi; Mohsen Madadi; Narayanaswamy Balakrishnan; Ahad Jamalizadeh
In this paper, a new mixture family of multivariate normal distributions, formed by mixing multivariate normal distribution and a skewed distribution, is constructed. Some properties of this family, such as characteristic function, moment generating function, and the first four moments are derived. The distributions of affine transformations and canonical forms of the model are also derived. An EM-type
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Robustness and asymptotics of the projection median J. Multivar. Anal. (IF 1.136) Pub Date : 2020-09-18 Kelly Ramsay; Stephane Durocher; Alexandre Leblanc
The projection median as introduced by Durocher and Kirkpatrick (2005); Durocher and Kirkpatrick (2009) is a robust multivariate, nonparametric location estimator. It is a weighted average of points in a sample, where each point’s weight is proportional to the fraction of directions in which that point is a univariate median. The projection median has the highest possible asymptotic breakdown and is
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Scale matrix estimation of an elliptically symmetric distribution in high and low dimensions J. Multivar. Anal. (IF 1.136) Pub Date : 2020-09-23 Anis M. Haddouche; Dominique Fourdrinier; Fatiha Mezoued
The problem of estimating the scale matrix Σ in a multivariate additive model, with elliptical noise, is considered from a decision-theoretic point of view. As the natural estimators of the form Σˆa=aS (where S is the sample covariance matrix and a is a positive constant) perform poorly, we propose estimators of the general form Σˆa,G=a(S+SS+G(Z,S)), where S+ is the Moore–Penrose inverse of S and G(Z
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Estimating an extreme Bayesian network via scalings J. Multivar. Anal. (IF 1.136) Pub Date : 2020-09-17 Claudia Klüppelberg; Mario Krali
A recursive max-linear vector models causal dependence between its components by expressing each node variable as a max-linear function of its parental nodes in a directed acyclic graph and some exogenous innovation. Motivated by extreme value theory, innovations are assumed to have regularly varying distribution tails. We propose a scaling technique in order to determine a causal order of the node
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Nonlinear and additive principal component analysis for functional data J. Multivar. Anal. (IF 1.136) Pub Date : 2020-09-09 Jun Song; Bing Li
We introduce a nonlinear additive functional principal component analysis (NAFPCA) for vector-valued functional data. This is a generalization of functional principal component analysis and allows the relations among the random functions involved to be nonlinear. The method is constructed via two additively nested Hilbert spaces of functions, in which the first space characterizes the functional nature
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Testing high dimensional covariance matrices via posterior Bayes factor J. Multivar. Anal. (IF 1.136) Pub Date : 2020-09-09 Zhendong Wang, Xingzhong Xu
With the advent of the era of big data, high dimensional covariance matrices are increasingly encountered and testing covariance structure has become an active area in contemporary statistical inference. Conventional testing methods fail when addressing high dimensional data due to the singularity of the sample covariance matrices. In this paper, we propose a novel test for the prominent identity test
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The consistency and asymptotic normality of the kernel type expectile regression estimator for functional data J. Multivar. Anal. (IF 1.136) Pub Date : 2020-09-09 Mustapha Mohammedi, Salim Bouzebda, Ali Laksaci
The aim of this paper is to nonparametrically estimate the expectile regression in the case of a functional predictor and a scalar response. More precisely, we construct a kernel-type estimator of the expectile regression function. The main contribution of this study is the establishment of the asymptotic properties of the expectile regression estimator. Precisely, we establish the almost complete
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A note on the regularity of optimal-transport-based center-outward distribution and quantile functions J. Multivar. Anal. (IF 1.136) Pub Date : 2020-08-28 Eustasio del Barrio, Alberto González-Sanz, Marc Hallin
We provide sufficient conditions under which the center-outward distribution and quantile functions introduced in Chernozhukov et al. (2017) and Hallin (2017) are homeomorphisms, thereby extending a recent result by Figalli (2018). Our approach relies on Caffarelli’s classical regularity theory for the solutions of the Monge–Ampère equation, but has to deal with difficulties related with the unboundedness
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On the structure of exchangeable extreme-value copulas J. Multivar. Anal. (IF 1.136) Pub Date : 2020-08-21 Jan-Frederik Mai, Matthias Scherer
We show that the set of d-variate symmetric stable tail dependence functions is a simplex and we determine its extremal boundary. The subset of elements which arises as d-margins of the set of (d+k)-variate symmetric stable tail dependence functions is shown to be proper for arbitrary k≥1. Finally, we derive an intuitive and useful necessary condition for a bivariate extreme-value copula to arise as
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Dimensionality reduction for binary data through the projection of natural parameters J. Multivar. Anal. (IF 1.136) Pub Date : 2020-08-19 Andrew J. Landgraf, Yoonkyung Lee
Principal component analysis (PCA) for binary data, known as logistic PCA, has become a popular alternative to dimensionality reduction of binary data. It is motivated as an extension of ordinary PCA by means of a matrix factorization, akin to the singular value decomposition, that maximizes the Bernoulli log-likelihood. We propose a new formulation of logistic PCA which extends Pearson’s formulation
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Single-index composite quantile regression for massive data J. Multivar. Anal. (IF 1.136) Pub Date : 2020-08-19 Rong Jiang, Keming Yu
Composite quantile regression (CQR) is becoming increasingly popular due to its robustness from quantile regression. Recently, the CQR method has been studied extensively with single-index models. However, the numerical inference of CQR methods for single-index models must involve iteration. In this study, we propose a non-iterative CQR (NICQR) estimation algorithm and derive the asymptotic distribution
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Testing for spherical and elliptical symmetry J. Multivar. Anal. (IF 1.136) Pub Date : 2020-08-17 Isaia Albisetti, Fadoua Balabdaoui, Hajo Holzmann
We construct new testing procedures for spherical and elliptical symmetry based on the characterization that a random vector X with finite mean has a spherical distribution if and only if E[u⊤X|v⊤X]=0 holds for any two perpendicular vectors u and v. Our test is based on the Kolmogorov–Smirnov statistic, and its rejection region is found via the spherically symmetric bootstrap. We show the consistency
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Bivariate gamma model J. Multivar. Anal. (IF 1.136) Pub Date : 2020-08-06 Ruijian Han, Kani Chen, Chunxi Tan
Among undirected graph models, the β-model plays a fundamental role and is widely applied to analyze network data. It assumes the edge probability is linked with the sum of the strength parameters of the two vertices through a sigmoid function. Because of the univariate nature of the link function, this formulation, despite its popularity, can be too restrictive for practical applications, even with
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Locally optimal designs for multivariate generalized linear models J. Multivar. Anal. (IF 1.136) Pub Date : 2020-08-06 Osama Idais
The multivariate generalized linear model is considered. Each univariate response follows a generalized linear model. In this situation, the linear predictors and the link functions are not necessarily the same. The quasi-Fisher information matrix is obtained by using the method of generalized estimating equations. Then locally optimal designs for multivariate generalized linear models are investigated
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Asymptotics and practical aspects of testing normality with kernel methods J. Multivar. Anal. (IF 1.136) Pub Date : 2020-08-04 Natsumi Makigusa, Kanta Naito
This paper is concerned with testing normality in a Hilbert space based on the maximum mean discrepancy. Specifically, we discuss the behavior of the test from two standpoints: asymptotics and practical aspects. Asymptotic normality of the test under a fixed alternative hypothesis is developed, which implies that the test has consistency. Asymptotic distribution of the test under a sequence of local
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Surface functional models J. Multivar. Anal. (IF 1.136) Pub Date : 2020-07-30 Ziqi Chen, Jianhua Hu, Hongtu Zhu
The aim of this paper is to develop a new framework of surface functional models (SFM) for surface functional data which contains repeated observations in two domains (typically, time-location). The primary problem of interest is to investigate the relationship between a response and the two domains, where the numbers of observations in both domains within a subject may be diverging. The SFMs are far
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Nonlinear functional canonical correlation analysis via distance covariance J. Multivar. Anal. (IF 1.136) Pub Date : 2020-07-29 Hanbing Zhu, Rui Li, Riquan Zhang, Heng Lian
Functional canonical correlation analysis (FCCA) is a tool for exploring the associations between a pair of functional data. However, when the association is nonlinear or even nonmonotone, FCCA can fail to discover any meaningful relationship between the pair. In this paper, nonlinear FCCA estimators are constructed based on some popular measures of dependence — distance covariance and distance correlation
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Copula-based regression models with data missing at random J. Multivar. Anal. (IF 1.136) Pub Date : 2020-07-22 Shigeyuki Hamori, Kaiji Motegi, Zheng Zhang
The existing literature of copula-based regression assumes that complete data are available, but this assumption is violated in many real applications. The present paper allows the regressand and regressors to be missing at random (MAR). We formulate a generalized regression model which unifies many prominent cases such as the conditional mean and quantile regressions. A semiparametric copula and the
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Estimating sparse networks with hubs J. Multivar. Anal. (IF 1.136) Pub Date : 2020-07-09 Annaliza McGillivray, Abbas Khalili, David A. Stephens
Graphical modelling techniques based on sparse estimation have been applied to infer complex networks in many fields, including biology and medicine, engineering, finance and social sciences. One structural feature of some of these networks that poses a challenge for statistical inference is the presence of a small number of strongly interconnected nodes, which are called hubs. For example, in microbiome
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Bayesian shrinkage estimation of negative multinomial parameter vectors J. Multivar. Anal. (IF 1.136) Pub Date : 2020-07-04 Yasuyuki Hamura, Tatsuya Kubokawa
The negative multinomial distribution is a multivariate generalization of the negative binomial distribution. In this paper, we consider the problem of estimating an unknown matrix of probabilities on the basis of observations of negative multinomial variables under the standardized squared error loss. First, a general sufficient condition for a shrinkage estimator to dominate the UMVU estimator is
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Multivariate tests of independence and their application in correlation analysis between financial markets J. Multivar. Anal. (IF 1.136) Pub Date : 2020-06-30 Long Feng, Xiaoxu Zhang, Binghui Liu
We consider the multivariate independence testing problem between pairs of random vectors for high-dimensional data and develop three high-dimensional nonparametric independence tests based on spatial sign and spatial rank, which have greater power than many existing popular tests, especially for heavy-tailed distributions. Under the elliptically symmetric distributions, which are much more general
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Scale and shape mixtures of matrix variate extended skew normal distributions J. Multivar. Anal. (IF 1.136) Pub Date : 2020-06-23 Amir Rezaei, Fatemeh Yousefzadeh, Reinaldo B. Arellano-Valle
In this paper, we propose a matrix extension of the scale and shape mixtures of multivariate skew normal distributions and present some particular cases of this new class. We also present several formal properties of this class, such as the marginal distributions, the moment generating function, the distribution of linear and quadratic forms, and the selection and stochastic representations. In addition
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A Conway–Maxwell-multinomial distribution for flexible modeling of clustered categorical data J. Multivar. Anal. (IF 1.136) Pub Date : 2020-06-15 Darcy Steeg Morris, Andrew M. Raim, Kimberly F. Sellers
Categorical data are often observed as counts resulting from a fixed number of trials in which each trial consists of making one selection from a prespecified set of categories. The multinomial distribution serves as a standard model for such data but assumes that trials are independent and identically distributed. Extensions such as the Dirichlet-multinomial and random-clumped multinomial distribution
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Testing for the significance of functional covariates J. Multivar. Anal. (IF 1.136) Pub Date : 2020-06-10 Samuel Maistre, Valentin Patilea
We consider the problem of testing for the nullity of conditional expectations of Hilbert space-valued random variables. We allow for conditioning variables taking values in finite or infinite Hilbert spaces. This testing problem occurs, for instance, when checking the goodness-of-fit or the effect of some infinite-dimensional covariates in regression models for functional data. Testing the independence
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Spearman rank correlation of the bivariate Student t and scale mixtures of normal distributions J. Multivar. Anal. (IF 1.136) Pub Date : 2020-06-10 Andréas Heinen, Alfonso Valdesogo
We derive an expression for the Spearman rank correlation of bivariate scale mixtures of normals (SMN) and we show that within this class, for any value of the correlation parameter, the Spearman rank correlation of the normal is the greatest in absolute value. We then provide expressions for the symmetric generalized hyperbolic, the Bessel, and the Laplace distributions. We further derive an expression
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Continuous time hidden Markov model for longitudinal data J. Multivar. Anal. (IF 1.136) Pub Date : 2020-06-10 Jie Zhou, Xinyuan Song, Liuquan Sun
Hidden Markov models (HMMs) describe the relationship between two stochastic processes, namely, an observed outcome process and an unobservable finite-state transition process. Given their ability to model dynamic heterogeneity, HMMs are extensively used to analyze heterogeneous longitudinal data. A majority of early developments in HMMs assume that observation times are discrete and regular. This
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Univariate likelihood projections and characterizations of the multivariate normal distribution J. Multivar. Anal. (IF 1.136) Pub Date : 2020-06-10 Albert Vexler
The problem of characterizing a multivariate distribution of a random vector using examination of univariate combinations of vector components is an essential issue of multivariate analysis. The likelihood principle plays a prominent role in developing powerful statistical inference tools. In this context, we raise the question: can the univariate likelihood function based on a random vector be used
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Computation of the expected Euler characteristic for the largest eigenvalue of a real non-central Wishart matrix J. Multivar. Anal. (IF 1.136) Pub Date : 2020-06-09 Nobuki Takayama, Lin Jiu, Satoshi Kuriki, Yi Zhang
We give an approximate formula for the distribution of the largest eigenvalue of real Wishart matrices by the expected Euler characteristic method for general dimension. The formula is expressed in terms of a definite integral with parameters. We derive a differential equation satisfied by the integral for the 2×2 matrix case and perform a numerical analysis of it.
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Linear orderings of the scale mixtures of the multivariate skew-normal distribution J. Multivar. Anal. (IF 1.136) Pub Date : 2020-06-06 Mehdi Amiri, Salman Izadkhah, Ahad Jamalizadeh
In this paper, (positive) linear stochastic orderings of random vectors X and Y having scale mixtures of the multivariate skew-normal distribution are studied. Necessary and sufficient convenient conditions for a⊤X to be less than a⊤Y, when a is a vector of positive values, in the sense of usual, convex and increasing convex stochastic orders are grasped. The results are potentially applied to conduct
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Uniform joint screening for ultra-high dimensional graphical models J. Multivar. Anal. (IF 1.136) Pub Date : 2020-06-06 Zemin Zheng, Haiyu Shi, Yang Li, Hui Yuan
Identifying large-scale conditional dependence structures through graphical models is a challenging yet practical problem. Under ultra-high dimensional settings, a screening procedure is generally suggested before variable selection to reduce computational costs. However, most existing screening methods examine the marginal correlations, thus not suitable to discover the conditional dependence in graphical
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Scalable interpretable learning for multi-response error-in-variables regression J. Multivar. Anal. (IF 1.136) Pub Date : 2020-06-06 Jie Wu, Zemin Zheng, Yang Li, Yi Zhang
Corrupted data sets containing noisy or missing observations are prevalent in various contemporary applications such as economics, finance and bioinformatics. Despite the recent methodological and algorithmic advances in high-dimensional multi-response regression, how to achieve scalable and interpretable estimation under contaminated covariates is unclear. In this paper, we develop a new methodology
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A procedure of linear discrimination analysis with detected sparsity structure for high-dimensional multi-class classification J. Multivar. Anal. (IF 1.136) Pub Date : 2020-06-01 Shan Luo, Zehua Chen
In this article, we consider discrimination analyses in high-dimensional cases where the dimension of the predictor vector diverges with the sample size in a theoretical setting. The emphasis is on the case where the number of classes is bigger than two. We first deal with the asymptotic misclassification rates of linear discrimination rules under various conditions. In practical high-dimensional classification
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Testing normality of data on a multivariate grid J. Multivar. Anal. (IF 1.136) Pub Date : 2020-05-28 Lajos Horváth, Piotr Kokoszka, Shixuan Wang
We propose a significance test to determine if data on a regular d-dimensional grid can be assumed to be a realization of Gaussian process. By accounting for the spatial dependence of the observations, we derive statistics analogous to sample skewness and kurtosis. We show that the sum of squares of these two statistics converges to a chi-square distribution with two degrees of freedom. This leads
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Sparsity-regularized skewness estimation for the multivariate skew normal and multivariate skew t distributions J. Multivar. Anal. (IF 1.136) Pub Date : 2020-05-27 Sheng Wang, Dale L. Zimmerman, Patrick Breheny
The multivariate skew normal (MSN) and multivariate skew t (MST) distributions have received considerable attention in the past two decades because of their appealing mathematical properties and their usefulness for modeling skewed data. We develop sparse regularization methodology for estimating the skewness parameters of these two distributions. This methodology facilitates skewness selection, i
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Polynomial traces and elementary symmetric functions in the latent roots of a non-central Wishart matrix J. Multivar. Anal. (IF 1.136) Pub Date : 2020-05-07 Elvira Di Nardo
Hypergeometric functions and zonal polynomials are the tools usually addressed in the literature to deal with the expected value of the elementary symmetric functions in non-central Wishart latent roots. The method here proposed recovers the expected value of these symmetric functions by using the umbral operator applied to the trace of suitable polynomial matrices and their cumulants. The employment
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Consistent Bayesian sparsity selection for high-dimensional Gaussian DAG models with multiplicative and beta-mixture priors J. Multivar. Anal. (IF 1.136) Pub Date : 2020-04-29 Xuan Cao, Kshitij Khare, Malay Ghosh
Estimation of the covariance matrix for high-dimensional multivariate datasets is a challenging and important problem in modern statistics. In this paper, we focus on high-dimensional Gaussian DAG models where sparsity is induced on the Cholesky factor L of the inverse covariance matrix. In recent work, (Cao et al., 2019), we established high-dimensional sparsity selection consistency for a hierarchical
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