Non-Asymptotic Analysis of Approximations for Multivariate Statistics

1. Auflage 2020
ISBN: 978-981-13-2615-8
Verlag: Springer Nature Singapore

Buch, Englisch, 130 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 224 g

Reihe: SpringerBriefs in 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, 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.

Zielgruppe

Research

Autoren/Hrsg.

Ulyanov, Vladimir V.

Fujikoshi, Yasunori

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen

Inhaltsverzeichnis

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.

Über Autor(innen)

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