Author | Kiefer, Jack Carl. author |
---|---|
Title | Introduction to Statistical Inference [electronic resource] / by Jack Carl Kiefer ; edited by Gary Lorden |
Imprint | New York, NY : Springer New York, 1987 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-9578-2 |
Descript | VIII, 334 p. online resource |
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: โNo Loss of Informationโ -- 6.5 Convex Loss -- 7 Point Estimation -- 7.1 Completeness and Unbiasedness -- 7.2 The โInformation Inequalityโ -- 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 โNormal Theoryโ 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