Overview
- Is the first book on non-asymptotic approximations and computable error bounds in multivariate analysis
- Focuses on the errors in high-dimensional approximations as well as large sample approximations for classical and modern multivariate statistics
- Suggests a general approach for construction of non-asymptotic bounds, illustrated by typical examples
Part of the book series: SpringerBriefs in Statistics (BRIEFSSTATIST)
Part of the book sub series: JSS Research Series in Statistics (JSSRES)
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Table of contents (11 chapters)
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Front Matter
Keywords
About this book
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.
Authors and Affiliations
About the authors
Ulyanov, Vladimir V., Moscow State University and HSE University, Moscow, Russia
Bibliographic Information
Book Title: Non-Asymptotic Analysis of Approximations for Multivariate Statistics
Authors: Yasunori Fujikoshi, Vladimir V. Ulyanov
Series Title: SpringerBriefs in Statistics
DOI: https://doi.org/10.1007/978-981-13-2616-5
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020
Softcover ISBN: 978-981-13-2615-8Published: 28 June 2020
eBook ISBN: 978-981-13-2616-5Published: 28 June 2020
Series ISSN: 2191-544X
Series E-ISSN: 2191-5458
Edition Number: 1
Number of Pages: IX, 130
Number of Illustrations: 16 b/w illustrations
Topics: Statistical Theory and Methods, Statistics and Computing/Statistics Programs, Applied Statistics