Non-Asymptotic Analysis of Approximations for Multivariate Statistics

by Yasunori Fujikoshi, Vladimir V. Ulyanov

Overview

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.

Product Details

ISBN-13:	9789811326158
Publisher:	Springer Nature Singapore
Publication date:	06/28/2020
Series:	SpringerBriefs in Statistics
Edition description:	1st ed. 2020
Pages:	130
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Fujikoshi, Yasunori, Hiroshima University, Higashi-Hiroshima, Japan

Ulyanov, Vladimir V., Moscow State University and HSE University, Moscow, Russia

Table of Contents

1. Introduction.- 2. Correlation Coefficient.- 3. MANOVA Test Statistics.- 4. Linear and Quadratic Discriminant Functions.- 5. Bootstrap Confidence Sets.- 6. Gaussian Comparison.- 7. Cornish-Fisher Expansions.- 8 Approximations for Statistics Based on Random Sample Sizes.- 9. Power-divergence Statistics.- 10.General Approach to Construct Non-asymptotic Bounds.- 11 - Other Topics.- Index.