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Professor Heinz Neudecker and matrix differential calculus
The late Professor Heinz Neudecker (1933–2017) made significant contributions to the development of matrix differential calculus and its applications...
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High-Dimensional Covariance Matrix Estimation An Introduction to Random Matrix Theory
This book presents covariance matrix estimation and related aspects of random matrix theory. It focuses on the sample covariance matrix estimator and...
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The Effect of the Prior and the Experimental Design on the Inference of the Precision Matrix in Gaussian Chain Graph Models
Here, we investigate whether (and how) experimental design could aid in the estimation of the precision matrix in a Gaussian chain graph model,...
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High-Dimensional Linear Models: A Random Matrix Perspective
Professor C.R.Rao’s Linear Statistical Inference is a classic that has motivated several generations of statisticians in their pursuit of theoretical...
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Random Graphical Model of Microbiome Interactions in Related Environments
The microbiome constitutes a complex microbial ecology of interacting components that regulates important pathways in the host. Most microbial...
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Tail probabilities of random linear functions of regularly varying random vectors
We provide a new extension of Breiman’s Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In...
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On the Baum–Katz theorem for randomly weighted sums of negatively associated random variables with general normalizing sequences and applications in some random design regression models
In this paper, we develop Jajte’s technique, which is used in the proof of strong laws of large numbers, to prove complete convergence for randomly...
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The asymptotic distribution of the condition number for random circulant matrices
In this manuscript, we study the limiting distribution for the joint law of the largest and the smallest singular values for random circulant...
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An Interesting Class of Non-Kac Random Polynomials
As evident from classical results on random polynomials, it is difficult to derive the probability distribution of the number of real roots
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A New Construction of Covariance Functions for Gaussian Random Fields
We develop a new approach to creating covariance functions for Gaussian random fields via point processes on the complex plane. We present two...
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Matrix-variate generalized linear model with measurement error
Matrix-variate generalized linear model (mvGLM) has been investigated successfully under the framework of tensor generalized linear model, because...
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Approximated Gaussian Random Field Under Different Parameterizations for MCMC
Fitting spatial models with a Gaussian random field as spatial random effect poses computational challenges for Markov Chain Monte Carlo (MCMC)...
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Normal Random Vectors
In this chapter, we consider normal random vectors in the real space. We first describe the pdf and cf of normal random vectors, and then consider...
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On the Rényi index of random graphs
Networks (graphs) permeate scientific fields such as biology, social science, economics, etc. Empirical studies have shown that real-world networks...
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Point process convergence for symmetric functions of high-dimensional random vectors
The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a...
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Robustness of Principal Component Analysis with Spearman’s Rank Matrix
This paper is concerned with robust principal component analysis (PCA) based on spatial sign and spatial rank vectors. The most common PC approach is...
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Inferential Tools for Assessing Dependence Across Response Categories in Multinomial Models with Discrete Random Effects
We propose a discrete random effects multinomial regression model to deal with estimation and inference issues in the case of categorical and...
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Jones-Balakrishnan Property for Matrix Variate Beta Distributions
Let
X andY be independent m × m symmetric positive definite random matrices. Assume thatX follows a matrix variate beta distribution with... -
V-optimality of designs in random effects Poisson regression models
The knowledge of the Fisher information is a fundamental tool to judge the quality of an experiment. Unlike in linear and generalized linear models...
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Mean test for high-dimensional data based on covariance matrix with linear structures
In this work, the mean test is considered under the condition that the number of dimensions p is much larger than the sample size n when the...
