Efficient algorithms for computing the distribution function, (log-)density function and for estimating the parameters of multivariate normal variance mixtures are introduced. For the evaluation of the distribution function, randomized quasi-Monte Carlo (RQMC) methods are utilized in a way that improves upon existing methods proposed for the special case of normal and t distributions. For evaluating

This paper proposes a new screening procedure for the ultrahigh dimensional data with a categorical response. By exploiting the group structure among predictors, a new partition-based screening approach is developed via the reproducing kernel Hilbert space (RKHS) embeddings in the maximum mean discrepancy framework. Consequently, the new method is able to identify the influential group of predictors

The goal of the optimal treatment regime is maximizing treatment benefits via personalized treatment assignments based on the observed patient and treatment characteristics. Parametric regression-based outcome learning approaches require exploring complex interplay between the outcome and treatment assignments adjusting for the patient and treatment covariates, yet correctly specifying such relationships

A great deal of literature has been established for regression analysis of longitudinal data but most of the existing methods assume that covariates can be observed completely or at the same observation times for the response variable, and the observation process is independent of the response variable completely or given covariates. As pointed out by many authors, in practice, one may face the situation

Data depth is a concept in multivariate statistics that measures the centrality of a point in a given data cloud in Rd. If the depth of a point can be represented as the minimum of the depths with respect to all one-dimensional projections of the data, then the depth satisfies the so-called projection property. Such depths form an important class that includes many of the depths that have been proposed

The expectation–maximization (EM) algorithm is a powerful computational technique for maximum likelihood estimation in incomplete data models. When the expectation step cannot be performed in closed form, a stochastic approximation of EM (SAEM) can be used. The convergence of the SAEM toward critical points of the observed likelihood has been proved and its numerical efficiency has been demonstrated

Maximizing modularity is a widely used method for community detection, which is generally solved by approximate or greedy search because of its high complexity. In this paper, we propose a method, named MSM, for modularity maximization, which reformulates the modularity maximization problem as a subset identification problem and maximizes the surrogate of the modularity. The surrogate of the modularity

The sum of Kronecker products (SKP) representation for spatial covariance matrices from gridded observations and a corresponding adaptive-cross-approximation-based framework for building the Kronecker factors are investigated. The time cost for constructing an n-dimensional covariance matrix is O(nk2) and the total memory footprint is O(nk), where k is the number of Kronecker factors. The memory footprint

Dimension reduction techniques for multivariate time series decompose the observed series into a few useful independent/orthogonal univariate components. A spectral domain method is developed for multivariate second-order stationary time series that linearly transforms the observed series into several groups of lower-dimensional multivariate subseries. These multivariate subseries have non-zero spectral

Discovery of localized and irregularly shaped anomalous patterns in spatial data provides useful context for operational decisions across many policy domains. The support vector subset scan (SVSS) integrates the penalized fast subset scan with a kernel support vector machine classifier to accurately detect spatial clusters without imposing hard constraints on the shape or size of the pattern. The method

In this paper, we discuss regression analysis of censored failure time data when there exist missing covariates and more specifically, we will consider interval-censored data, a general form of censored data, and the nonignorable missing. Although many methods have been proposed in the literature for censored data with missing covariates, they only apply to limited situations and it does not seem to

Spatial count data models are used to explain and predict the frequency of phenomena such as traffic accidents in geographically distinct entities such as census tracts or road segments. These models are typically estimated using Bayesian Markov chain Monte Carlo (MCMC) simulation methods, which, however, are computationally expensive and do not scale well to large datasets. Variational Bayes (VB)

A Bayesian approach is proposed that unifies Gaussian Bayesian network constructions and comparisons between two networks (identical or differential) for data with graph ordering unknown. When sampling graph ordering, to escape from local maximums, an adjusted single queue equi-energy algorithm is applied. The conditional posterior probability mass function for network differentiation is derived and

Factor analysis is a statistical technique for data reduction and structure detection that traditionally relies on the normality assumption for factors. However, due to the presence of non-normal features such as asymmetry and heavy tails in many practical situations, the first two moments cannot adequately explain the factors. An extension of the factor analysis model is introduced by assuming a generalization

Multivariate functional data are frequently obtained in many scientific or industrial areas where several functions for a statistical unit are observed over time. It is often interesting to check if the mean vector functions of two multivariate functional samples are equal. To address this important issue, two global tests for the above two-sample problem for multivariate functional data are proposed

Nowadays, it has become increasingly common to store large-scale data sets distributedly across a great number of clients. The aim of the study is to develop a distributed estimator for generalized linear models (GLMs) in the “large n, diverging pn” framework with a weak assumption on the number of clients. When the dimension diverges at the rate of o(n), the asymptotic efficiency of the global maximum

A simulation–extrapolation procedure has been developed for estimating the regression coefficients in a class of parametric modal regression models when the covariates are prone to measurement errors. Large sample properties of the proposed estimator, including the consistency and asymptotic normality, have been thoroughly investigated. Simulation studies and real data applications have been conducted

In modern pharmaceutical studies, treatments may include several drugs added sequentially, and the drugs’ order-of-addition can have significant impacts on their efficacy. In practice, experiments enumerating all possible drug sequences are often not affordable, and appropriate statistical models which can accurately predict all cases using only a small number of experimental trials are required. A

Stochastic differential equation mixed-effects models (SDEMEMs) are flexible hierarchical models that are able to account for random variability inherent in the underlying time-dynamics, as well as the variability between experimental units and, optionally, account for measurement error. Fully Bayesian inference for state-space SDEMEMs is performed, using data at discrete times that may be incomplete

This paper considers the estimation of high dimensional factor model with multiple threshold-type regime shifts in factor loadings. Firstly, the number of thresholds is determined by comparing the number of factors in the adjacent subintervals. Secondly, the thresholds are estimated one by one by concentrated least squares, and then the factors and loadings are obtained by the principal component method

Multivariate regression techniques are commonly applied to explore the associations between large numbers of outcomes and predictors. In real-world applications, the outcomes are often of mixed types, including continuous measurements, binary indicators, and counts, and the observations may also be incomplete. Building upon the recent advances in mixed-outcome modeling and sparse matrix factorization

Recently, it has been shown that the shape of a marginal distribution can be more accurately and efficiently captured using a set of low discrepancy sequence (LDS) points compared to standard grid points. This suggests that the use of LDS could improve the approximation to marginal posterior distributions produced by grid-based Bayesian methods such as the Integrated Nested Laplace Approximation (INLA)

Preclinical experiment on two-drug combination is a stepping stone to multi-drug combination studies. Experimental designs have been proposed in the literature to test the presence of synergism between the combined drugs. However, a design that is efficient for synergy testing is not necessarily desirable for dose–response modeling and the latter is important for future development on drug interaction

The bivariate normal multilevel model (MLM) provides a flexible modeling framework for cost-effectiveness analyses (CEAs) alongside cluster randomized trials (CRTs) as well as for sample size calculations of these trials. The bivariate MLM assumes a joint normal distribution for effects and costs, both within (individual level) and between (cluster level) clusters. A typical problem in CEAs is that

Quantile regression is an important tool in data analysis. Linear regression, or more generally, parametric quantile regression imposes often too restrictive assumptions. Nonparametric regression avoids making distributional assumptions, but might have the disadvantage of not exploiting distributional modelling elements that might be brought in. A semiparametric approach towards estimating conditional

The semi-varying coefficient models are widely used in the application of finance, economics, medical science and many other areas. In general, the functional coefficients are estimated by local smoothing methods, e.g. local linear estimator. So the computation cost is severe because one should point-wisely estimate the value of a coefficient function. In this paper, we give an insight into the trade-off

Sequential and temporal data arise in many fields of research, such as quantitative finance, medicine, or computer vision. A novel approach for sequential learning, called the signature method and rooted in rough path theory, is considered. Its basic principle is to represent multidimensional paths by a graded feature set of their iterated integrals, called the signature. This approach relies critically

Comparing the accuracy and the behaviour of different diagnostic procedures is one of the main objectives of the Receiver Operating Characteristic (ROC) curve analysis. Along with the diagnostic variables it is usual to observe other covariates, but that extra information has been hardly ever considered for the comparison of this kind of curves. A new non-parametric test is proposed for the comparison

A new multivariate extension of Kendall’s dependence coefficient tailored for use in regression analysis is introduced. This coefficient is called Kendall regression coefficient and indicates how well the response variable can be approximated by a strictly increasing function of the regressor (predictor) variables. The properties of this coefficient are examined. In the second part the empirical regression

To estimate distribution functions and quantiles of a response variable when the data having nonignorable nonresponse and the dimension of covariate is not low, this article assumes that the propensity follows a general semiparametric model, but the distribution of the response variable and related covariates is unspecified. To address the identifiability problem, an instrumental covariate, which is

A method for dealing with multivariate analysis of marked spatio-temporal point processes is presented by introducing different partial point characteristics, and by extending the spatial dependence graph model formalism. The approach yields a unified framework for different types of spatio-temporal data, including both, purely qualitatively (multivariate) cases and multivariate cases with additional

Relational count data are often obtained from sources such as simultaneous purchase in online shops and social networking service information. Clustering such relational count data reveals the latent structure of the relationship between objects such as household items or people. When relational count data observed at multiple time points are available, it is worthwhile incorporating the time structure

Multivariate regression has many applications, ranging from time series prediction to genomics. Borrowing information across the outcomes can improve prediction error, even when outcomes are statistically independent. Many methods exist to implement this strategy, for example the multiresponse lasso, but choosing the optimal method for a given dataset is difficult. These issues are addressed by establishing

Categorical responses cause no conceptual complications for dimension reduction in regression, but the performance of some methods may suffer in this context and hence supervised dimension reduction in practice must recognize the nature of the response. Using a continuous latent variable to represent an unobserved response underlying the binary response, a joint model is proposed for dimension reduction

Modeling the interactions of competing risks that affect the occurrence of various decrements such as death or disease is an essential issue in survival analysis and actuarial science. Popular assumptions for the construction of decrement models are uniform distributions of decrements in a multiple decrement table (mUDD) and associated single decrement tables (sUDD), respectively. Even though there

In longitudinal data with many replications, the high-order autoregressive (AR) structure of covariance matrix is required to capture the serial correlations between repeated outcomes. Thus, the high-order AR structure requires many parameters underlying the dynamic data dependence. In this paper, we proposed an autoregressive moving-average (ARMA) structure of covariance matrix involving multivariate

In this paper, we consider the estimation method for the partially linear single-index model with endogenous regressors in the linear part. The Generalized Method of Moments (GMM) using instrumental variables is applied to cope with the problem that the parameter estimators may be inconsistent due to endogeneity. The GMM estimation is based on an iterative procedure, which has generalized the well

Discovery of causal relationships from observational data is an important problem in many areas. Several recent results have established the identifiability of causal directed acyclic graphs (DAGs) with non-Gaussian and/or nonlinear structural equation models (SEMs). Focusing on nonlinear SEMs defined by non-invertible functions, which exist in many data domains, a novel test is proposed for non-invertible

Many real-world classification problems come with costs which can vary for different types of misclassification. It is thus important to develop cost-sensitive classifiers which minimize the total misclassification cost. Although binary cost-sensitive classifiers have been well-studied, solving multicategory classification problems is still challenging. A popular approach to address this issue is to

Variable selection for failure time data with a cured fraction has been discussed by many authors but most of existing methods apply only to right-censored failure time data. In this paper, we consider variable selection when one faces interval-censored failure time data arising from a general class of generalized odds rate mixture cure models, and we propose a penalized variable selection method by

Dynamical systems describe changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for the drivers and impediments of the processes. Extracting these governing equations from data is a central challenge in many diverse areas of science and engineering

A novel approach is proposed for density estimation on a network. Nonparametric density estimation on a network is formulated as a nonparametric regression problem by binning. Nonparametric regression using local polynomial kernel-weighted least squares have been studied rigorously, and its asymptotic properties make it superior to kernel estimators such as the Nadaraya–Watson estimator. When applied

Gaussian process (GP) models are widely used to analyze spatially referenced data and to predict values at locations without observations. They are based on a statistical framework, which enables uncertainty quantification of the model structure and predictions. Both the evaluation of the likelihood and the prediction involve solving linear systems. Hence, the computational costs are large and limit

In many complex systems studied in statistical physics, inter-arrival times between events such as solar flares, trades and neuron voltages follow a heavy-tailed distribution. The set of event times is fractal-like, being dense in some time windows and empty in others, a phenomenon which has been dubbed “bursty”. A new model for the inter-exceedance times of such events above high thresholds is proposed

Linear regression with normally distributed errors – including particular cases such as ANOVA, Student’s t-test or location–scale inference – is a widely used statistical procedure. In this case the ordinary least squares estimator possesses remarkable properties but is very sensitive to outliers. Several robust alternatives have been proposed, but there is still significant room for improvement. An

In many application areas, the problem of the automatic variable selection in a linear model with asymmetric errors is encountered, when the number of explanatory variables diverges with the sample size. For this high-dimensional model, the penalized least squares method is not appropriate and the quantile framework makes the inference more difficult because of the non differentiability of the loss

A smooth simultaneous confidence band (SCB) is constructed for the distribution of unobserved errors in a nonparametric regression model based on a plug-in kernel distribution estimator. The normalized estimation error process is shown to converge to a Gaussian process. Simulation experiments indicate that the proposed SCB not only strikes an intelligent balance between coverage probability and precision

Regression models are widely used statistical procedures, and the validation of their assumptions plays a crucial role in the data analysis process. Unfortunately, validating assumptions usually depends on the availability of tests tailored to the specific model of interest. A novel Bayesian goodness-of-fit hypothesis testing approach is presented for a broad class of regression models the response

Outer power (OP) transformations of Archimedean generators are suggested to increase the modeling flexibility and statistical fitting capabilities of classical Archimedean copulas restricted to a single parameter. For OP-transformed Archimedean copulas, a formula for computing tail dependence coefficients is obtained, as well as two feasible OP Archimedean copula estimators are proposed and their properties

Quantifying the serial correlation across time lags is a crucial step in the identification and diagnosis of a time series model. Simple and partial autocorrelation functions of the time series are the most widely used tools for this purpose with scalar time series. Nevertheless, there is a lack of an established method for the identification of functional time series (FTS) models. Functional versions

An extension of the D-vine based forward regression procedure to a R-vine forward regression is proposed. In this extension any R-vine structure can be taken into account. Moreover, a new heuristic is proposed to determine which R-vine structure is the most appropriate to model the conditional distribution of the response variable given the covariates. It is shown in the simulation that the performance

Imputation and the inverse probability weighting are two commonly used approaches in missing data analysis. Parametric versions of them are not robust due to model misspecification of some unknown functions. Nonparametric ones are robust but are impractical when the number of covariates is large due to the problem of “curse of dimension”. A beyond multiple robust method is proposed in this paper. This

Sufficient dimension reduction (SDR) using distance covariance (DCOV) was recently proposed as an approach to dimension-reduction problems. Compared with other SDR methods, it is model-free without estimating link function and does not require any particular distributions on predictors. However, the DCOV-based SDR method involves optimizing a nonsmooth and nonconvex objective function over the Stiefel

Modeling longitudinal binary data is challenging but common in practice. Existing methods on modeling of binary responses take no account of the fact that the correlation coefficient of binary responses must have an upper bound which is smaller than one. Ignoring this fact can lead to incorrect statistical inferences for longitudinal binary data. A novel method is proposed to model the mean and within-subject

The EM algorithm is a widely applicable algorithm for modal estimation but often criticized for its slow convergence. A new hybrid accelerator named APX-EM is proposed for speeding up the convergence of EM algorithm, which is based on both Linearly Preconditioned Nonlinear Conjugate Gradient (PNCG) and PX-EM algorithm. The intuitive idea is that, each step of the PX-EM algorithm can be viewed approximately

Spatial dependent data frequently occur in spatial econometrics and endemiology. In this work, we propose a class of penalized robust regression estimators based on exponential squared loss with independent and identical distributed errors for general spatial autoregressive models. A penalized exponential squared loss with the adaptive lasso penalty is employed for simultaneous model selection and

The majority of methods available to model survival data only deal with right censoring. However, there are many applications where left, right and/or interval censoring simultaneously occur. A methodology that is capable of handling all types of censoring as well as flexibly estimating several types of covariate effects is presented. The baseline hazard is modelled through monotonic P-splines. The

A self-calibrated direct estimation algorithm based on ℓ1-regularized quadratic programming is proposed. The self-calibration is achieved by an iterative algorithm for finding the regularization parameter simultaneously with the estimation target. The proposed algorithm is free of cross-validation. Two applications of this algorithm are proposed, namely precision matrix estimation and linear discriminant

The incident/dynamic time-dependent AUC (Area Under the ROC Curve) is an appealing measure to express the discriminative value of a dynamic survival model over time. However, estimation of this measure is not straightforward. Four recently proposed estimation approaches are studied. In an extensive simulation study, a head-to-head comparison between these four estimation methods is made. The estimation

Latent block models are used for probabilistic biclustering, which is shown to be an effective method for analyzing various relational data sets. However, there has been no statistical test method for determining the row and column cluster numbers of latent block models. Recent studies have constructed statistical-test-based methods for stochastic block models, which assume that the observed matrix