Symmetric positive definite matrix data commonly appear in computer vision and medical imaging, such as diffusion tensor imaging. The aim of this paper is to develop a nonparametric estimation method for a symmetric positive definite matrix regression function given covariates. By obtaining a suitable parametrization based on the Cholesky decomposition, we make it possible to apply univariate smoothing

In this work, we introduce a local linear nonparametric estimation of the regression function of a censored scalar response random variable, given a functional random covariate. Under standard conditions, we establish the pointwise and the uniform almost-complete convergences, with rates, of the proposed estimator. Then, we carry out a simulation study and a real data analysis in order to compare the

In this paper, we consider rank estimation for partial functional linear regression models based on functional principal component analysis. The proposed rank-based method is robust to outliers in the errors and highly efficient under a wide range of error distributions. The asymptotic properties of the resulting estimators are established under some regularity conditions. A simulation study conducted

Large-scale data from various research fields are not only heterogeneous and sparse but also difficult to store on a single machine. Expectile regression is a popular alternative for modeling heterogeneous data. In this paper, we devise a distributed optimization approach to SCAD and adaptive LASSO penalized expectile regression, where the observations are randomly partitioned across multiple machines

We propose a new time varying correlation coefficient, which is a local correlation measure of a pair of time series. The time varying correlation coefficient is locally estimated using a nonparametric kernel method. Asymptotic normality of the estimated time varying correlation is established, which allows us to construct statistical methods of confidence interval and hypothesis tests. Finite sample

When data for a completely randomised design are categorical rather than continuous, the Cochran–Mantel–Haenszel suite of tests may be applied, albeit that there is only one stratum. In introductory design courses this design, and the randomised block design, are usually the first designs introduced. Using the completely randomised design instead of the randomised block design ignores blocks (strata)

Bayesian nonparametric statistics is an area of considerable research interest. While recently there has been an extensive concentration in developing Bayesian nonparametric procedures for model checking, the use of the Dirichlet process, in its simplest form, along with the Kullback–Leibler divergence is still an open problem. This is mainly attributed to the discreteness property of the Dirichlet

In this paper, we investigate the adequate check of the parametric Tobit model. A Cramér–Von Mises type test statistic is constructed, and its asymptotic properties under the null and alternative hypotheses are rigorously studied. The method is effective for the adequacy check of parametric regression models with a scalar or multivariate covariate. Furthermore, it avoids the nonparametric smoothing

The original version of this article unfortunately contained a mistake.

Multivariate longitudinal data is often encountered in the jobs of statisticians and practitioners. It is challenging to model the covariance matrix due to the complex structure of correlations among multiple responses. For this modeling task, several effective Cholesky decomposition based methods have been studied. However, direct interpretation of the covariation structure among multiple responses

This paper introduces a new class of distributions, named length-biased Weibull mixtures, in order to deal with heavy-tailed data encountered in quantitative risk modeling. As a generalization of the Erlang mixtures with common scale parameter, our proposed class possesses attractive modeling features such as flexibility to fit various distributional shapes and weak denseness in the class of distributions

We propose a fully Bayesian methodology for estimation of functions that have jump discontinuities. The proposed model is an extension of the LARK model, which enables functions to be represented by the small number of elements from an overcomplete system. In the proposed model, multiple kernels are used as the elements of an overcomplete system. Since these elements are composed of different types

We study the strong oracle property of concave penalized estimators in the high-dimensional linear regression model for a class of concave penalties that have infinite derivative at the origin. The class includes the bridge and log penalties as typical examples. It is known that infinite derivative of the penalty is not a problem for the weak oracle property but prevents the strong oracle property

To model and forecast a monthly pine sawtimber (PST) stumpage price, \(y_t\), data collected across 11 southern states in the U.S., we adopt a new semiparametric approach where the first phase adopts a nonparametric method called “Time Series Central Subspace with Covariates” (TSCS-C) to extract sufficient information about \(y_t\) through a univariate time series \(\{d_t\}\), which is a linear combination

In this paper, we obtain the weakly asymptotic formulas of the tail probabilities of randomly weighted sums and their maximum of dominated varying-tailed random variables under a general conditional dependence structure, where the corresponding random weights can take values in the whole real space. The obtained results extend and improve some existing ones. An application of the weakly asymptotic

The stick-breaking representation is one of the fundamental properties of the Dirichlet process. It represents the random probability measure as a discrete random sum whose weights and atoms are formed by independent and identically distributed sequences of beta variates and draws from the normalized base measure of the Dirichlet process parameter. It is used extensively in posterior simulation for

Underdispersed and overdispersed phenomena are often observed in practice. To deal with these phenomena, we introduce a new thinning-based integer-valued autoregressive process. Some probabilistic and statistical properties of the process are obtained. The asymptotic normality of the estimators of the model parameters, using conditional least squares, weighted conditional least squares and modified

Recently, Yoo (Statistics 50:1086–1099, 2016) newly defines an informative predictor subspace to contain the central subspace. The method to estimate the informative predictor subspace does not require any of the conditions assumed to hold in usual sufficient dimension reduction methodologies. However, like sliced inverse regression (Li in J Am Stat Assoc 86:316–342, 1991) and sliced average variance

This paper introduces a new class of barrier options and its variations. We call the new class of options as two-asset alternating barrier options, since we consider alternating barrier levels for two underlying assets. The alternating barrier levels are placed in the sub-periods of the option’s lifetime; each being applied to one of the two underlying assets. We also consider vertical branches of

Progressive censoring is essential for researchers in industry as a mean to remove subjects before the final termination point in order to save time and reduce cost. Recently, kernel density estimation has been intensively investigated due to its asymptotic properties and applications. In this paper, we investigate the asymptotic properties of the kernel density estimators based on progressive type-II

Bayes factors, practical tools of applied statistics, have been dealt with extensively in the literature in the context of hypothesis testing. The Bayes factor based on parametric likelihoods can be considered both as a pure Bayesian approach as well as a standard technique to compute p-values for hypothesis testing. We employ empirical likelihood methodology to modify Bayes factor type procedures

This paper provides an overview of two semiparametric estimation methods recently proposed in the literature for the accelerated failure time mixture cure model. We prove that the two estimation methods are asymptotically equivalent. A simulation is conducted to investigate the rate of convergence of the two methods. We apply these methods to fit the accelerated failure time mixture cure model to the

In stratified case-cohort designs, samplings of case-cohort samples are conducted via a stratified random sampling based on covariate information available on the entire cohort members. In this paper, we extended the work of Kang & Cai (2009) to a generalized stratified case-cohort study design for failure time data with multiple disease outcomes. Under this study design, we developed weighted estimating

This is discussion on "A general approach to D-optimal designs for weighted univariate polynomial regression models" by Holger Dette and Matthias Trampisch.

In studies of complex disorders such as nicotine dependence, it is common that researchers assess multiple variables related to a disorder as well as other disorders that are potentially correlated with the primary disorder of interest. In this work, we refer to those variables and disorders broadly as multiple traits. The multiple traits may or may not have a common causal genetic variant. Intuitively

Nowadays, Bayesian methods are routinely used for estimating parameters of item response theory (IRT) models. However, the marginal likelihoods are still rarely used for comparing IRT models due to their complexity and a relatively high dimension of the model parameters. In this paper, we review Monte Carlo (MC) methods developed in the literature in recent years and provide a detailed development