Shrinkage Estimation for Mean and Covariance Matrices

ebook SpringerBriefs in Statistics

By Hisayuki Tsukuma

cover image of Shrinkage Estimation for Mean and Covariance Matrices

Sign up to save your library

With an OverDrive account, you can save your favorite libraries for at-a-glance information about availability. Find out more about OverDrive accounts.

   Not today

Find this title in Libby, the library reading app by OverDrive.

Download Libby on the App Store Download Libby on Google Play

Search for a digital library with this title

Title found at these libraries:

Library Name Distance
Loading...

This book provides a self-contained introduction to shrinkage estimation for matrix-variate normal distribution models. More specifically, it presents recent techniques and results in estimation of mean and covariance matrices with a high-dimensional setting that implies singularity of the sample covariance matrix. Such high-dimensional models can be analyzed by using the same arguments as for low-dimensional models, thus yielding a unified approach to both high- and low-dimensional shrinkage estimations. The unified shrinkage approach not only integrates modern and classical shrinkage estimation, but is also required for further development of the field. Beginning with the notion of decision-theoretic estimation, this book explains matrix theory, group invariance, and other mathematical tools for finding better estimators. It also includes examples of shrinkage estimators for improving standard estimators, such as least squares, maximum likelihood, and minimum risk invariantestimators, and discusses the historical background and related topics in decision-theoretic estimation of parameter matrices. This book is useful for researchers and graduate students in various fields requiring data analysis skills as well as in mathematical statistics.

Shrinkage Estimation for Mean and Covariance Matrices