Improving Efficiency by Shrinkage

Marvin Gruber

• Introduction to shrinkage estimators: the Stein paradox; the ridge estimators of Hoerl and Kennard. Estimation for a single linear model: the James-Stein estimator for a single model; ridge estimators from different general points of view; improving the James-Stein estimator - the positive parts. Other linear model setups: the simultaneous estimation problem; precision of individual estimators; the multivariate model; other linear model setups.

"The author has done a great job in writing the materials. The book is more on the theoretical and mathematical side than on the application side. The estimators and the results discussed in the book will be useful to practitioners in the physical, chemical, and engineering sciences. The book is a very good addition to the literature on James-Stein and ridge estimators. "---Technometrics". . .an essential library purchase. "---Short Book Reviews of the International Statistical Institute". . .recommended as a textbook for graduate students. . .[and] as a research monograph for professionals in statistics, engineering and econometrics who are interested to know how to improve upon the traditional estimators in regressional analysis."---Statistical Papers