Linear Regression

1. Front Matter

   Pages I-XII

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2. Point Estimation and Linear Regression

   1. Front Matter

      Pages 1-1

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   2. Fundamentals

      • Jürgen Groß

      Pages 3-31

   3. The Linear Regression Model

      • Jürgen Groß

      Pages 33-86

3. Alternatives to Least Squares Estimation

   1. Front Matter

      Pages 87-87

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   2. Alternative Estimators

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      Pages 89-211

   3. Linear Admissibility

      • Jürgen Groß

      Pages 213-256

4. Miscellaneous Topics

   1. Front Matter

      Pages 257-257

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   2. The Covariance Matrix of the Error Vector

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      Pages 259-291

   3. Regression Diagnostics

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      Pages 293-329

   4. Matrix Algebra

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      Pages 331-358

   5. Stochastic Vectors

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      Pages 359-367

   6. An Example Analysis with R

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      Pages 369-379

5. Back Matter

   Pages 381-397

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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.

• Covariance matrix
• Estimator
• Least Squares
• Point Estimation
• Regression
• Variance
• linear regression

• Department of Statistics, University of Dortmund, Dortmund, Germany

  Jürgen Groß

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