Adaptive Regression

Linear regression is an important area of statistics, theoretical or applied. There have been a large number of estimation methods proposed and developed for linear regression. Each has its own competitive edge but none is good for all purposes. This manuscript focuses on construction of an adaptive combination of two estimation methods. The purpose of such adaptive methods is to help users make an objective choice and to combine desirable properties of two estimators. "Since 1757, when Roger Joseph Boscovich addressed the fundamental mathematical problem in determining the parameters which best fits observational equations, a large number of estimation methods has been proposed and developed for linear regression. Four of the commonly used methods are the least absolute deviations, least squares, trimmed least squares, and the M-regression. Each of these methods has its own competitive edge but none is good for all purposes. This book focuses on construction of an adaptive combination of several pairs of these estimation methods. The purpose of adaptive methods is to help users make an objective choice and combine desirable properties of two estimators.". "With this single objective in mind, this book describes in detail the theory, method, and algorithm 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.". "The 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."--BOOK JACKET. Front Matter....Pages i-xii Prologue....Pages 1-10 Regression Methods....Pages 11-36 Adaptive LAD + LS Regression....Pages 37-60 Adaptive LAD + TLS Regression....Pages 61-74 Adaptive LAD + M-Regression....Pages 75-86 Adaptive LS + TLS Regression....Pages 87-98 Adaptive Choice of Trimming....Pages 99-114 Adaptive Combination of Tests....Pages 115-124 Computational Aspects....Pages 125-142 Some Asymptotic Results....Pages 143-156 Epilogue....Pages 157-158 Back Matter....Pages 159-177 While there have been a large number of estimation methods proposed and developed for linear regression, none has proved good for all purposes. This text focuses on the construction of an adaptive combination of two estimation methods so as to help users make an objective choice and combine the desirable properties of two estimators.