Adaptive Regression Book

Adaptive Regression is intended for researchers and students of statistics who are interested in adaptive estimation and testing and their mathematical properties in the context of linear regression. There have been a large number of estimation methods proposed and developed for linear regression. Each has its advantages but none is good for all purposes. This book focuses on the construction of an adaptive combination of two estimation methods. The purpose of such adaptive methods is to help users make an objective choice and combine desirable properties of two estimators. With this objective in mind, this book describes in detail the theory, method and algorithms for combining several pairs of estimation methods. It will be of interest for those who wish to perform regression analyses beyond the least squares method, and for researchers in robust statistics and graduate students who wish to learn some asymptotic theory for linear models. In addition to a review of least squares, ridge, the least absolute deviations, and the M-, L-, and GM-regressions, this book covers four new estimators:* Least absolute deviations with the least squares regression* Least absolute deviations with M-regression* Least absolute deviations with trimmed least squares * Least squares with trimmed least squares regressionThe methods presented in this book are illustrated on numerical examples based on real data. The computer programs in S-PLUS for all procedures presented are available for data analysts working with applications in industry, economics and the experimental sciences. Yadolah Dodge is Professor of Statistics and Operations Research at the University of Neuchtel, Switzerland. He is the author of Analysis of Experiments with Missing Data (John Wiley), Statistique: Dictionnaire-Encyclopdique (Dunod), Analyse de Rgression Applique (Dunod) and co-author of Mathematical Programming in Statistics (John Wiley, Classic Edition) with T. S. Arthanari and Alternative Methods of Regression (John Wiley) with David Birkes. He is a fellow of the Royal Statistical Society and a member of the International Statistical Institute. He has served as the Special Issue Editor and on the Advisory Board of Computational Statistics and Data Analysis for several years. Jana Jurecov is Professor of Probability and Mathematical Statistics at Charles University in Prague, Czech Rebublic. She is a member of the Bernoulli Society Council and a Fellow of the Institute of Mathematical Statistics. An Associate Editor of the Annals of Statistics for eight years, she is on the board of five other international statistical journals. She was nominated as titular for the Chaire Francqui Interuniversitaire by three Belgian Universities for the academic year 1999-2000 and is co-author with P. K. Sen of Robust Statistical Procedures: Asymptotics and Inter-Relations.Read More