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High Dimensional Probability VII

Part of the Progress in Probability Book Series (volume 71)

Editors: Houdré, Christian; Mason, David M.; Reynaud-Bouret, Patricia; Rosiński, Jan

DOI: 10.1007/978-3-319-40519-3

ISBN: 978-3-319-40517-9

Publisher: Springer International Publishing - Springer Journals

Sep 22, 2016

11 - 19 of 19 Chapters

LitStream

Limit Theorems for Quantile and Depth Regions for Stochastic Processes

Kuelbs, James; Zinn, Joel

Pages: 255 –280

[Since contours of multi-dimensional depth functions often characterize the distribution, it has become of interest to consider structural properties and limit theorems for the sample contours [see Zuo and Serfling (Ann. Stat. 28(2):483–499, 2000) and Kong and Mizera (Stat. Sin. 22(4):1589–1610,...
LitStream

In Memory of Wenbo V. Li’s Contributions

Shao, Qi-Man

Pages: 281 –291

[Wenbo V. Li was Professor of Mathematical Sciences at the University of Delaware. He died of a heart attack in January 2013. Wenbo made significant contributions to many of the areas in which he worked, especially to small value probability estimates. This note is a brief survey of Wenbo V. Li’s...
LitStream

Orlicz Integrability of Additive Functionals of Harris Ergodic Markov Chains

Adamczak, Radosław; Bednorz, Witold

Pages: 295 –326

[For a Harris ergodic Markov chain (Xn)n ≥ 0, on a general state space, started from the small measure or from the stationary distribution, we provide optimal estimates for Orlicz norms of sums ∑i = 0τf(Xi), where τ is the first regeneration time of the chain. The estimates are expressed in terms...
LitStream

Bounds for Stochastic Processes on Product Index Spaces

Bednorz, Witold

Pages: 327 –357

[In this paper we discuss the question of how to bound the supremum of a stochastic process with an index set of a product type. It is tempting to approach the question by analyzing the process on each of the marginal index sets separately. However it turns out that it is necessary to also study...
LitStream

Permanental Vectors and Selfdecomposability

Eisenbaum, Nathalie

Pages: 359 –362

[Exponential variables, gamma variables or squared centered Gaussian variables, are always selfdecomposable. Does this property extend to multivariate gamma distributions? We show here that for any d-dimensional centered Gaussian vector (η1, …, ηd) with a nonsingular covariance, the vector (η12,...
LitStream

Permanental Random Variables, M-Matrices and α-Permanents

Marcus, Michael B.; Rosen, Jay

Pages: 363 –379

[We explore some properties of a recent representation of permanental vectors which expresses them as sums of independent vectors with components that are independent gamma random variables.]
LitStream

Convergence in Law Implies Convergence in Total Variation for Polynomials in Independent Gaussian, Gamma or Beta Random Variables

Nourdin, Ivan; Poly, Guillaume

Pages: 381 –394

[Consider a sequence of polynomials of bounded degree evaluated in independent Gaussian, Gamma or Beta random variables. We show that, if this sequence converges in law to a nonconstant distribution, then (1) the limit distribution is necessarily absolutely continuous with respect to the Lebesgue...
LitStream

Perturbation of Linear Forms of Singular Vectors Under Gaussian Noise

Koltchinskii, Vladimir; Xia, Dong

Pages: 397 –423

[Let A∈ℝm×n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$A \in...
LitStream

Optimal Kernel Selection for Density Estimation

Lerasle, Matthieu; Magalhães, Nelo Molter; Reynaud-Bouret, Patricia

Pages: 425 –460

[We provide new general kernel selection rules thanks to penalized least-squares criteria. We derive optimal oracle inequalities using adequate concentration tools. We also investigate the problem of minimal penalty as described in Birgé and Massart (2007, Probab. Theory Relat. Fields,...

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