EAN: 9789819960767

SPRINGERBRIEFS IN STATISTICS STEIN ESTIMATION...

This book provides a self-contained introduction of Stein shrinkage estimation for the mean
vector of a multivariate normal distribution. The book begins with a brief discussion of basic
notions and results from decision theory such as admissibility  minimaxity  and (generalized)
Bayes estimation. It also presents Stein's unbiased risk estimator and the James-Stein
estimator in the first chapter. In the following chapters  the authors consider estimation of
the mean vector of a multivariate normal distribution in the known and unknown scale case when
the covariance matrix is a multiple of the identity matrix and the loss is scaled squared
error. The focus is on admissibility  inadmissibility  and minimaxity of (generalized) Bayes
estimators  where particular attention is paid to the class of (generalized) Bayes estimators
with respect to an extended Strawderman-type prior. For almost all results of this book  the
authors present a self-contained proof. The book is helpful for researchers and graduate
students in various fields requiring data analysis skills as well as in mathematical
statistics.

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