Fujikoshi Y., Ulyanov V.V. Non-Asymptotic Analysis of Approximations for Multivariate Statistics

Springer, 2020. — 133 p. — (SpringerBriefs in Statistics). — ISBN: 978-981-13-2615-8.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 the computable error bounds on correlation coefficients, MANOVA tests and discriminant functions studied in recent papers. It then introduces new areas of research in high-dimensional approximations for bootstrap procedures, Cornish–Fisher expansions, power-divergence statistics and approximations of statistics based on observations with random sample size. Lastly, 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.Non-Asymptotic Bounds
Scale-Mixed Distributions
MANOVA Test Statistics
Linear and Quadratic Discriminant Functions
Cornish–Fisher Expansions
Likelihood Ratio Tests with Box-Type Moments
Bootstrap Confidence Sets
Gaussian Comparison and Anti-concentration
Approximations for Statistics Based on Random Sample Sizes
Power-Divergence Statistics
General Approach to Constructing Non-Asymptotic Bounds