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Random Matrix Time Series
In this paper, a time series model is proposed, where the coefficients take values from random matrix ensembles. Formal definitions, theoretical...
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Matrix-Variate Hidden Markov Regression Models: Fixed and Random Covariates
Two families of matrix-variate hidden Markov regression models (MV-HMRMs) are here introduced. The distinction between them relies on the role of the...
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Covariance matrix testing in high dimension using random projections
Estimation and hypothesis tests for the covariance matrix in high dimensions is a challenging problem as the traditional multivariate asymptotic...
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Normality test in random coefficient autoregressive models
In this paper, we consider the problem of testing for normality of the two unobservable random processes included in the first order random...
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Wavelet Shrinkage Estimation for Mean Matrix of Matrix-Variate Elliptically Contoured Distributions
Finding the appropriate threshold is one of the most important issues in the wavelet shrinkage method. Especially when the goal is to estimate the...
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Matrix variate density estimation with additional information
Quite often, some additional information is available from different sources other than the parent population. In such cases, the density estimation...
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Random Forests
Bagging refers to fitting a learning algorithm on bootstrap samples and aggregating the results. A random forest performs bagging of trees, and in...
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On Survival of Coherent Systems Subject to Random Shocks
We consider coherent systems subject to random shocks that can damage a random number of components of a system. Based on the distribution of the...
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A Random-Coefficients Analysis with a Multivariate Random-Coefficients Linear Model
Random-coefficients linear models can be considered as a particular case of linear mixed models. Different sources of variation are treated by random...
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Matrix quadratic risk of orthogonally invariant estimators for a normal mean matrix
In estimation of a normal mean matrix under the matrix quadratic loss, we develop a general formula for the matrix quadratic risk of orthogonally...
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An adaptive singular value shrinkage for estimation problem of low-rank matrix mean with unknown covariance matrix
Matrix models which are constructed from a deterministic signal plus noise are used in variety of fields. In particular, it commonly happens that a...
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Comparison of extreme order statistics from two sets of heterogeneous dependent random variables under random shocks
In this paper, we consider two k -out-of- n systems comprising heterogeneous dependent components under random shocks, with an Archimedean copula. We...
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Random Variables and Expectations
Random experiments have sample spaces may not consist of numbers. For instance, in a coin-tossing experiment, the sample space consists of the...
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Generalized mixed spatiotemporal modeling with a continuous response and random effect via factor analysis
This work focuses on Generalized Linear Mixed Models that incorporate spatiotemporal random effects structured via Factor Model (FM) with nonlinear...
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Random Vectors
We consider the concept and applications of random vectors in this chapter. In describing the probabilistic properties of a random vector, we need to...
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Extremes of Markov random fields on block graphs: Max-stable limits and structured Hüsler–Reiss distributions
We study the joint occurrence of large values of a Markov random field or undirected graphical model associated to a block graph. On such graphs,...
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Statistics in Matrix Notation
Let us consider an \({N \times n}\) data matrix...
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Multiple Random Variables and Joint Distributions
Multiple r.v.s are often involved in various random experiments. For instance, an educator might examine the joint behavior of study time and grades,...