We consider copulas with a given diagonal section and compute the explicit density of the unique optimal copula which maximizes the entropy. In this sense, this copula is the least informative among the copulas with a given diagonal section. We give an explicit criterion on the diagonal section...

The tail copula is widely used to describe the dependence in the tail of multivariate distributions. In some situations such as risk management, the dependence structure may be linked with some covariate. The tail copula thus depends on this covariate and is referred to as the conditional tail...

In this paper, we introduce a matrix variate slash distribution as a scale mixture of the matrix variate normal and the uniform distributions. We study some properties of the proposed distribution and give maximum likelihood (ML) estimators of its parameters using EM algorithm. We provide an...

Inference about dependence in a multiway data array can be made using the array normal model, which corresponds to the class of multivariate normal distributions with separable covariance matrices. Maximum likelihood and Bayesian methods for inference in the array normal model have appeared in...

Let (εj)j≥0 be a sequence of independent p-dimensional random vectors and τ≥1 a given integer. From a sample ε1,…,εT+τ of the sequence, the so-called lag-τ auto-covariance matrix is Cτ=T−1∑j=1Tετ+jεjt. When the dimension p is large compared to the sample size T, this paper...

In this article we develop a test statistic for testing the equality of mean vectors for paired doubly multivariate observations with q response variables and u sites in blocked compound symmetric covariance matrix setting. We obtain a natural extension of the Hotelling’s T2 statistic, the...

Differential entropy and log determinant of the covariance matrix of a multivariate Gaussian distribution have many applications in coding, communications, signal processing and statistical inference. In this paper we consider in the high-dimensional setting optimal estimation of the...

Varying-coefficient models are useful extension of classical linear models. This paper is concerned with the statistical inference of varying-coefficient regression models with autoregressive errors. By combining the estimated residuals, the smoothly clipped absolute deviation (SCAD) penalty and...

In this article, a novel adaptive estimation is proposed for varying coefficient models. Unlike the traditional least squares based methods, the proposed approach can adapt to different error distributions. An efficient EM algorithm is provided to implement the proposed estimation. The...

It is well known that the F-test breaks down completely when the dimension of covariates exceeds the sample size. This paper proposes a new test for part of regression coefficients in high dimensional linear models. Under the high dimensional null hypothesis and various scenarios of the...