Non-Asymptotic Analysis of Approximations for Multivariate Statistics

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, CornishFisher 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.

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

Autorentext
Fujikoshi, Yasunori, Hiroshima University, Higashi-Hiroshima, Japan
Ulyanov, Vladimir V., Moscow State University and HSE University, Moscow, Russia

Inhalt

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.