Overview
- First book to explore Shrinkage Estimation as a global phenomenon
- Focuses on point and loss estimation in multivariate normal and spherically symmetric distributions
- Authors are at the forefront of Shrinkage research
Part of the book series: Springer Series in Statistics (SSS)
Buy print copy
About this book
Chapter 2 is concerned with estimating the mean vector of a multivariate normal distribution under quadratic loss from a frequentist perspective. In Chapter 3 the authors take a Bayesian view of shrinkage estimation in the normal setting. Chapter 4 introduces the general classes of spherically and elliptically symmetric distributions. Point and loss estimation for these broad classes are studied in subsequent chapters. In particular, Chapter 5 extends many of the results from Chapters 2 and 3 to spherically and elliptically symmetric distributions.
Chapter 6 considers the general linear model with spherically symmetric error distributions when a residual vector is available. Chapter 7 then considers the problem of estimating a location vector which is constrained to lie in a convex set. Much of the chapter is devoted to one of two types of constraint sets, balls and polyhedral cones. In Chapter 8 the authors focus on loss estimation and data-dependent evidence reports.
Appendices cover a number of technical topics including weakly differentiable functions; examples where Stein’s identity doesn’t hold; Stein’s lemma and Stokes’ theorem for smooth boundaries; harmonic, superharmonic and subharmonic functions; and modified Bessel functions.
Similar content being viewed by others
Keywords
Table of contents (8 chapters)
Reviews
“The well-written volume, presenting the actual knowledge in this field, is suitable for readers having good background in analysis, linear algebra, probability theory and mathematical statistics.” (Kurt Marti, zbMATH 1411.62011, 2019)
Authors and Affiliations
About the authors
Martin T. Wells is the Charles A. Alexander Professor of Statistical Sciences at Cornell University. He is also a Professor of Social Statistics, Professor of Biostatistics and Epidemiology at Weill Cornell Medicine as well as an Elected Member of the Cornell Law School Faculty. He is a fellow of both the Institute of Mathematical Statistics and American Statistical Society and an Elected Member, International Statistical Institute. His research interests include Bayesian statistics, biostatistics, decision theory, empirical legal studies, machine learning, and statistical genomics.
Bibliographic Information
Book Title: Shrinkage Estimation
Authors: Dominique Fourdrinier, William E. Strawderman, Martin T. Wells
Series Title: Springer Series in Statistics
DOI: https://doi.org/10.1007/978-3-030-02185-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-030-02184-9Published: 06 December 2018
eBook ISBN: 978-3-030-02185-6Published: 27 November 2018
Series ISSN: 0172-7397
Series E-ISSN: 2197-568X
Edition Number: 1
Number of Pages: XIII, 333
Number of Illustrations: 1 b/w illustrations