Introduction to Statistical Inference
This book is based upon lecture notes developed by Jack Kiefer for a course in statistical inference he taught at Cornell University. The notes were distributed to the class in lieu of a textbook, and the problems were used for homework assignments. Relying only on modest prerequisites of probabilit...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
1987, 1987
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| Edition: | 1st ed. 1987 |
| Series: | Springer Texts in Statistics
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| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Introduction to Statistical Inference
- 2 Specification of a Statistical Problem
- 2.1 Additional Remarks on the Loss Function
- 3 Classifications of Statistical Problems
- 4 Some Criteria for Choosing a Procedure
- 4.1 The Bayes Criterion
- 4.2 Minimax Criterion
- 4.3 Randomized Statistical Procedures
- 4.4 Admissibility: The Geometry of Risk Points
- 4.5 Computation of Minimax Procedures
- 4.6 Unbiased Estimation
- 4.7 The Method of Maximum Likelihood
- 4.8 Sample Functionals: The Method of Moments
- 4.9 Other Criteria
- 5 Linear Unbiased Estimation
- 5.1 Linear Unbiased Estimation in Simple Settings
- 5.2 General Linear Models: The Method of Least Squares
- 5.3 Orthogonalization
- 5.4 Analysis of the General Linear Model
- 6 Sufficiency
- 6.1 On the Meaning of Sufficiency
- 6.2 Recognizing Sufficient Statistics
- 6.3 Reconstruction of the Sample
- 6.4 Sufficiency: “No Loss of Information”
- 6.5 Convex Loss
- 7 Point Estimation
- 7.1 Completeness and Unbiasedness
- 7.2 The “Information Inequality”
- 7.3 Invariance
- 7.4 Computation of Minimax Procedures (Continued)
- 7.5 The Method of Maximum Likelihood
- 7.6 Asymptotic Theory
- 8 Hypothesis Testing
- 8.1 Introductory Notions
- 8.2 Testing Between Simple Hypotheses
- 8.3 Composite Hypotheses: UMP Tests; Unbiased Tests
- 8.4 Likelihood Ratio (LR) Tests
- 8.5 Problems Where n Is to Be Found
- 8.6 Invariance
- 8.7 Summary of Common “Normal Theory” Tests
- 9 Confidence Intervals
- Appendix A Some Notation, Terminology, and Background Material
- Appendix B Conditional Probability and Expectation, Bayes Computations
- Appendix C Some Inequalities and Some Minimization Methods
- C.1 Inequalities
- C.2 Methods of Minimization
- References