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Non-Asymptotic Analysis of Approximations for Multivariate Statistics

  • Yasunori Fujikoshi
  • Vladimir V. Ulyanov
Book
  • 392 Downloads

Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)

Also part of the JSS Research Series in Statistics book sub series (JSSRES)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Yasunori Fujikoshi, Vladimir V. Ulyanov
    Pages 1-4
  3. Yasunori Fujikoshi, Vladimir V. Ulyanov
    Pages 5-21
  4. Yasunori Fujikoshi, Vladimir V. Ulyanov
    Pages 23-33
  5. Yasunori Fujikoshi, Vladimir V. Ulyanov
    Pages 35-47
  6. Yasunori Fujikoshi, Vladimir V. Ulyanov
    Pages 49-59
  7. Yasunori Fujikoshi, Vladimir V. Ulyanov
    Pages 61-71
  8. Yasunori Fujikoshi, Vladimir V. Ulyanov
    Pages 73-80
  9. Yasunori Fujikoshi, Vladimir V. Ulyanov
    Pages 81-91
  10. Yasunori Fujikoshi, Vladimir V. Ulyanov
    Pages 93-107
  11. Yasunori Fujikoshi, Vladimir V. Ulyanov
    Pages 109-116
  12. Yasunori Fujikoshi, Vladimir V. Ulyanov
    Pages 117-130

About this book

Introduction

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.

 

Keywords

Multivariate Statistics Non-asymptotic Analysis Computable Error Bounds Edgeworth Expansions Cornish-Fisher Expansions

Authors and affiliations

  • Yasunori Fujikoshi
    • 1
  • Vladimir V. Ulyanov
    • 2
  1. 1.Hiroshima UniversityHigashi-HiroshimaJapan
  2. 2.National Research University Higher School of EconomicsMoscow State UniversityMoscowRussia

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