Linear Regression [Paperback]

The book covers the basic theory of linear regression models and presents a comprehensive survey of different estimation techniques as alternatives and complements to least squares estimation. Proofs are given for the most relevant results, and the presented methods are illustrated with the help of numerical examples and graphics. Special emphasis is placed on practicability and possible applications. The book is rounded off by an introduction to the basics of decision theory and an appendix on matrix algebra.

In linear regression the ordinary least squares estimator plays a central role and sometimes one may get the impression that it is the only reasonable and applicable estimator available. Nonetheless, there exists a variety of alterna? tives, proving useful in specific situations. Purpose and Scope. This book aims at presenting a comprehensive survey of different point estimation methods in linear regression, along with the the? oretical background on a advanced courses level. Besides its possible use as a companion for specific courses, it should be helpful for purposes of further reading, giving detailed explanations on many topics in this field. Numerical examples and graphics will aid to deepen the insight into the specifics of the presented methods. For the purpose of self-containment, the basic theory of linear regression models and least squares is presented. The fundamentals of decision theory and matrix algebra are also included. Some prior basic knowledge, however, appears to be necessary for easy reading and understanding.I Point Estimation and Linear Regression.- Fundamentals.- 1.1 Linear Models.- 1.1.1 Application of Linear Models.- 1.1.2 Types of Linear Models.- 1.1.3 Proceeding with Linear Models.- 1.1.4 A Preliminary Example.- 1.2 Decision Theory and Point Estimation.- 1.2.1 Decision Rule.- 1.2.2 Non-operational Decision Rule.- 1.2.3 Loss and Risk.- 1.2.4 Choosing a Decision Rule.- 1.2.5 Admissibility.- 1.2.6 Squared Error LosslSd