Ebook: Linear Regression

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.

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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. The relationship between different estimators is clearly described and categories of estimators are worked out in detail. 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 laid on the practicability, and possible applications are discussed. The book is rounded off by an introduction to the basics of decision theory and an appendix on matrix algebra.

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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. The relationship between different estimators is clearly described and categories of estimators are worked out in detail. 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 laid on the practicability, and possible applications are discussed. The book is rounded off by an introduction to the basics of decision theory and an appendix on matrix algebra.

Content:
Front Matter....Pages I-XII
Front Matter....Pages 1-1
Fundamentals....Pages 3-31
The Linear Regression Model....Pages 33-86
Front Matter....Pages 87-87
Alternative Estimators....Pages 89-211
Linear Admissibility....Pages 213-256
Front Matter....Pages 257-257
The Covariance Matrix of the Error Vector....Pages 259-291
Regression Diagnostics....Pages 293-329
Matrix Algebra....Pages 331-358
Stochastic Vectors....Pages 359-367
An Example Analysis with R....Pages 369-379
Back Matter....Pages 381-397

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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. The relationship between different estimators is clearly described and categories of estimators are worked out in detail. 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 laid on the practicability, and possible applications are discussed. The book is rounded off by an introduction to the basics of decision theory and an appendix on matrix algebra.

Content:
Front Matter....Pages I-XII
Front Matter....Pages 1-1
Fundamentals....Pages 3-31
The Linear Regression Model....Pages 33-86
Front Matter....Pages 87-87
Alternative Estimators....Pages 89-211
Linear Admissibility....Pages 213-256
Front Matter....Pages 257-257
The Covariance Matrix of the Error Vector....Pages 259-291
Regression Diagnostics....Pages 293-329
Matrix Algebra....Pages 331-358
Stochastic Vectors....Pages 359-367
An Example Analysis with R....Pages 369-379
Back Matter....Pages 381-397
....