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Distributional regression is extended to Gaussian response vectors of dimension greater than two by parameterizing the covariance matrix $\Sigma$ of the response distribution using the entries of its Cholesky decomposition. The more common…

Methodology · Statistics 2025-10-07 Thomas Muschinski , Georg J. Mayr , Thorsten Simon , Nikolaus Umlauf , Achim Zeileis

Functional Gaussian graphical models (GGM) used for analyzing multivariate functional data customarily estimate an unknown graphical model representing the conditional relationships between the functional variables. However, in many…

Methodology · Statistics 2024-10-03 Debangan Dey , Sudipto Banerjee , Martin Lindquist , Abhirup Datta

In this paper we study the problem of testing the null hypothesis that errors from k independent parametrically specified generalized autoregressive conditional heteroskedasticity (GARCH) models have the same distribution versus a general…

Statistics Theory · Mathematics 2008-12-05 Ajay Chandra

Multivariate categorical data occur in many applications of machine learning. One of the main difficulties with these vectors of categorical variables is sparsity. The number of possible observations grows exponentially with vector length,…

Machine Learning · Statistics 2015-03-10 Yarin Gal , Yutian Chen , Zoubin Ghahramani

Consider sample covariance matrices of the form $Q:=\Sigma^{1/2} X X^\top \Sigma^{1/2}$, where $X=(x_{ij})$ is an $n\times N$ random matrix whose entries are independent random variables with mean zero and variance $N^{-1}$, and $\Sigma$ is…

Probability · Mathematics 2023-06-09 Fan Yang

We introduce a Bayesian approach for multivariate spatio-temporal prediction for high-dimensional count-valued data. Our primary interest is when there are possibly millions of data points referenced over different variables, geographic…

Methodology · Statistics 2015-12-24 Jonathan R. Bradley , Scott H. Holan , Christopher K. Wikle

We introduce state-space models where the functionals of the observational and the evolutionary equations are unknown, and treated as random functions evolving with time. Thus, our model is nonparametric and generalizes the traditional…

Methodology · Statistics 2014-02-24 Anurag Ghosh , Soumalya Mukhopadhyay , Sandipan Roy , Sourabh Bhattacharya

Maximum-type statistics of certain functions of the sample covariance matrix of high-dimensional vector time series are studied to statistically confirm or reject the null hypothesis that a data set has been collected under normal…

Statistics Theory · Mathematics 2023-10-13 Ansgar Steland

This paper explores the possibility of establishing an analytic form of the distribution of the order parameter fluctuations in a two-dimensional critical spin wave model, or width fluctuations of a two dimensional Edwards-Wilkinson…

Statistical Mechanics · Physics 2022-04-13 Steven T. Bramwell

In this note, we claim that diagonal scaling of a sample covariance matrix is asymptotically inconsistent if the ratio of the dimension to the sample size converges to a positive constant, where population is assumed to be Gaussian with a…

Statistics Theory · Mathematics 2018-08-20 Tomonari Sei

We consider the problem of constructing nonparametric undirected graphical models for high-dimensional functional data. Most existing statistical methods in this context assume either a Gaussian distribution on the vertices or linear…

Statistics Theory · Mathematics 2021-03-22 Eftychia Solea , Holger Dette

In this paper, we analyze the relative errors that crop up in the various reliability measures due to the tacit assumption that the components are independently working associated with a $n$-component series system or a parallel system…

Statistics Theory · Mathematics 2025-03-28 Subarna Bhattacharjee , Aninda Kumar Nanda , Subhashree Patra

We study the problem of learning mixtures of $k$ Gaussians in $d$ dimensions. We make no separation assumptions on the underlying mixture components: we only require that the covariance matrices have bounded condition number and that the…

Data Structures and Algorithms · Computer Science 2024-11-20 Sitan Chen , Vasilis Kontonis , Kulin Shah

Many statistical applications require the quantification of joint dependence among more than two random vectors. In this work, we generalize the notion of distance covariance to quantify joint dependence among d >= 2 random vectors. We…

Methodology · Statistics 2018-06-18 Shubhadeep Chakraborty , Xianyang Zhang

This paper takes a different approach for the distributed linear parameter estimation over a multi-agent network. The parameter vector is considered to be stochastic with a Gaussian distribution. The sensor measurements at each agent are…

Systems and Control · Electrical Eng. & Systems 2022-04-19 Subhro Das

We consider the notion of the matrix (tensor) distribution of a measurable function of several variables. On the one hand, it is an invariant of this function with respect to a certain group of transformations of variables; on the other…

Dynamical Systems · Mathematics 2023-11-03 A. Vershik

Consider informative selection of a sample from a finite population. Responses are realized as independent and identically distributed (i.i.d.) random variables with a probability density function (p.d.f.) f, referred to as the…

Statistics Theory · Mathematics 2012-11-26 Daniel Bonnéry , F. Jay Breidt , François Coquet

Generating large-scale samples of stationary random fields is of great importance in the fields such as geomaterial modeling and uncertainty quantification. Traditional methodologies based on covariance matrix decomposition have the…

Methodology · Statistics 2022-08-23 Bin Zhu , Jiahao Liu , Zhengshou Lai , Tao Qian

The empirical probability density function for the conditional distribution of the true value of Poisson distribution parameter on one measurement is constructed by computer experiment. The analysis of the obtained distributions confirms…

Data Analysis, Statistics and Probability · Physics 2009-11-10 S. I. Bityukov , V. A. Medvedev , V. V. Smirnova , Yu. V. Zernii

We consider large non-Hermitian random matrices $X$ with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are asymptotically Gaussian for test functions having…

Probability · Mathematics 2023-10-16 Giorgio Cipolloni , László Erdős , Dominik Schröder