Titlebook: Non-Asymptotic Analysis of Approximations for Multivariate Statistics; Yasunori Fujikoshi,Vladimir V. Ulyanov Book 2020 The Author(s), und

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hemorrhage

Scale-Mixed Distributions,ar as sampling distributions of various statistics such as the studentized version of some estimators. Errors of the approximation are evaluated in . and .-norms. Extension to multivariate scale mixtures with error bounds evaluated in .-norm shall be discussed in Chap.?..

GLARE

Book 2020stly, it proposes a general approach for the construction of non-asymptotic bounds, providing relevant examples for several complicated statistics. It is a valuable resource for researchers with a basic understanding of multivariate statistics...?.

refraction

2191-544X ional approximations as well as large sample approximations .This book presents recent non-asymptotic results for approximations in multivariate statistical analysis. The book is unique in its focus on results with the correct error structure for all the parameters involved. Firstly, it discusses th

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狗窩

MANOVA Test Statistics,ted in .-norm. The error bound is given for the limiting distribution of . by using a relationship between . and .. Further, we give error bounds for these criteria when the sample size and the dimension are large.

法律

condone

Gaussian Comparison and Anti-concentration,a the Kullback–Leibler divergence. We also establish an anti-concentration bound for a squared norm of a non-centered Gaussian element in a Hilbert space. A number of examples are also provided, motivating the results and its applications to statistical inference and high-dimensional CLT.

CUB

ARCH

Power-Divergence Statistics,the rate of convergence is of order . with .. Under some conditions . is close to 1. The proofs are based on the fundamental number theory results about approximating the number of integer points in convex sets by the Lebesgue measure of the set.