Penalty, Shrinkage and Pretest Strategies

The objective of this book is to compare the statistical properties of penalty and non-penalty estimation strategies for some popular models. Specifically, it considers the full model, submodel, penalty, pretest and shrinkage estimation techniques for three regression models before presenting the asymptotic properties of the non-penalty estimators and their asymptotic distributional efficiency comparisons. Further, the risk properties of the non-penalty estimators and penalty estimators are explored through a Monte Carlo simulation study. Showcasing examples based on real datasets, the book will be useful for students and applied researchers in a host of applied fields.

The book’s level of presentation and style make it accessible to a broad audience. It offers clear, succinct expositions of each estimation strategy. More importantly, it clearly describes how to use each estimation strategy for the problem at hand. The book is largely self-contained, as are the individual chapters, so that anyone interested in a particular topic or area of application may read only that specific chapter. The book is specially designed for graduate students who want to understand the foundations and concepts underlying penalty and non-penalty estimation and its applications. It is well-suited as a textbook for senior undergraduate and graduate courses surveying penalty and non-penalty estimation strategies, and can also be used as a reference book for a host of related subjects, including courses on meta-analysis. Professional statisticians will find this book to be a valuable reference work, since nearly all chapters are self-contained.

“The objective of this book is to lay the foundation for shrinkage-type estimators and to compare statistical properties of penalty and non penalty estimation strategies for some popular linear models. … Undoubtedly this volume will serve as an excellent textbook for advanced undergraduate and graduate courses involving penalty and non penalty estimation and as a references source for professional statisticians and practitioners.” (Vyacheslav Lyubchich, Technometrics, Vol. 57 (1), February, 2015)

“The book’s goal is to present some shrinkage, penalty and pretest estimation techniques for different models (e.g., normal, Poisson, multiple regression, etc.). Selected penalty estimation techniques are compared with the full model, sub-model, pretest, and shrinkage estimators in the regression case. The book is dedicated to graduate students, researchers and practitioners in this field.” (Marina Gorunescu, zbMATH 1306.62002, 2015)

“This book is a comprehensive and well-illustrated overview of the developments in this area in the last decade. … the book is a very good source for those who want to start research in the area of preliminary test and Stein-type estimation in the direction of penalty estimation using a priori information. It will also be of interest and immense help to those interested in the theoretical as well as applied aspects of pretesting, shrinkage and penalty estimation.” (Shalabh, Mathematical Reviews, August, 2014)

Ejaz Ahmed is a Professor and Dean of the Faculty of Math and Science at Brock University. Prior to joining Brock, he was a professor and head of Mathematics at the University of Windsor and University of Regina, having previously held a faculty position at the University of Western Ontario. His areas of expertise include statistical inference, shrinkage estimation, high dimensional data and asymptotic theory. He has published over 135 articles in scientific journals, been thesis advisor of eleven Ph.D. students, held over 150 scholarly presentations and reviewed over 100 books. Further, he has authored/coauthored six books and served as a Board of Director and Chairman of the Education Committee of the Statistical Society of Canada and VP Communication for ISBIS. His research activities and work have been recognized in his election as a Fellow of the American Statistical Association, selection as member of an Evaluation Group, Discovery Grants and the Grant Selection Committee,Natural Sciences and Engineering Research Council of Canada, and by serving as an editor/associate editor of many statistical journals, including SPL and CSDA and as a book review editor for Technometrics.