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We give a decomposition of the posterior predictive variance using the law of total variance and conditioning on a finite dimensional discrete random variable. This random variable summarizes various features of modeling that are used to…
The purpose of the present paper is to establish moderate deviation principles for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of the theory of large deviations…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
This note develops Rio's proof [C. R. Math. Acad. Sci. Paris, 1995] of the rate of convergence in the Marcinkiewicz--Zygmund strong law of large numbers to the case of sums of dependent random variables with regularly varying normalizing…
In this paper, we consider the problem of simultaneous testing of multivariate normal means under arbitrary covariance dependence. Specifically, let $\boldsymbol{X}\sim N_n(\boldsymbol{\theta},\boldsymbol{\Sigma})$, where…
We prove a Poisson limit theorem in the total variation distance of functionals of a general Poisson point process using the Malliavin-Stein method. Our estimates only involve first and second order difference operators and are closely…
Non-uniform estimates are obtained for Poisson, compound Poisson, translated Poisson, negative binomial and binomial approximations to sums of of m-dependent integer-valued random variables. Estimates for Wasserstein metric also follow…
In this paper, we develop a non-asymptotic local normal approximation for multinomial probabilities. First, we use it to find non-asymptotic total variation bounds between the measures induced by uniformly jittered multinomials and the…
Mark-point dependence plays a critical role in research problems that can be fitted into the general framework of marked point processes. In this work, we focus on adjusting for mark-point dependence when estimating the mean and covariance…
The topic of this paper is the asymptotic distribution of random orthogonal matrices distributed according to Haar measure. We examine the total variation distance between the joint distribution of the entries of $W_n$, the $p_n \times q_n$…
This article compares the distributions of integer-valued random variables and Poisson random variables. It considers the total variation and the Wasserstein distance and provides, in particular, explicit bounds on the pointwise difference…
The $W$-random graphs provide a flexible framework for modeling large random networks. Using the Large Deviation Principle (LDP) for $W$-random graphs from [9], we prove the LDP for the corresponding class of random symmetric…
We introduce a family of local inhomogeneous mark-weighted summary statistics, of order two and higher, for general marked point processes. Depending on how the involved weight function is specified, these summary statistics capture…
Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of…
We analyze the extreme value dependence of independent, not necessarily identically distributed multivariate regularly varying random vectors. More specifically, we propose estimators of the spectral measure locally at some time point and…
We give necessary and sufficient conditions to characterize the convergence in distribution of a sequence of arbitrary random variables to a probability distribution which is the invariant measure of a diffusion process. This class of…
The problem of inferring the distribution of a random vector given that its norm is large requires modeling a homogeneous limiting density. We suggest an approach based on graphical models which is suitable for high-dimensional vectors. We…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…
A sample covariance matrix $\boldsymbol{S}$ of completely observed data is the key statistic in a large variety of multivariate statistical procedures, such as structured covariance/precision matrix estimation, principal component analysis,…
We provide non-asymptotic, relative deviation bounds for the eigenvalues of empirical covariance and Gram matrices in general settings. Unlike typical uniform bounds, which may fail to capture the behavior of smaller eigenvalues, our…