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Lecture Notes



Lecture Notes

The lecture notes are part of a book in progress by Professor Dudley. Please refer to the calendar section for reading assignments for this course. Professor Dudley welcomes comments, corrections, and suggestions, which can be sent to him via the OCW Feedback form.




Chapter 1: Decision Theory and Testing Simple Hypotheses

1.1 Deciding between Two Simple Hypotheses: The Neyman-Pearson Lemma, 8 pages. (PDF)
1.2 Decision Theory, 6 pages. (PDF)
1.3 Bayes Decision Theory, 6 pages. (PDF)
1.4* Realizable Rules, 2 pages. (PDF)
1.5 The Sequential Probability Ratio Test, 5 pages. (PDF)
1.6 Sequential Decision Theory, 2 pages. (PDF)
1.7 Proof of Optimality of the SPRT, 9 pages. (PDF)


Chapter 2: Sufficiency and Estimation

2.1 Sufficient Statistics, 8 pages. (PDF)
2.2 Estimation and Convexity, 5 pages. (PDF)
2.3 Minimal Sufficiency and the Lehmann-Scheffé Property, 6 pages. (PDF)
2.4 Lower Bounds on Mean-squared Errors: Information Inequalities, 10 pages. (PDF)
2.5 Exponential Families, 13 pages. (PDF)
2.6 Bayes Estimation, 5 pages. (PDF)
2.7 Stein's Phenomenon and James-Stein Estimators, 5 pages. (PDF)
2.8* Continuity at the Boundary for Exponential Families, 3 pages. (PDF)


Chapter 3: Bayes, Maximum Likelihood and M-estimation

3.1 Maximum Likelihood Estimates - In Exponential Families, 4 pages. (PDF)
3.2 Likelihood Equations and Errors-in-variables Regression: Solari's Example, 5 pages. (PDF)
3.3 M-estimators and Their Consistency, 8 pages. (PDF)
3.4 M-estimates and Robust Location Estimates, 8 pages. (PDF)
3.44 Robustness, Breakdown Points, and 1-dimensional Location M-estimates, 6 pages. (PDF)
3.5 Consistency of Approximate M-estimators of psi type, 4 pages. (PDF)
3.6 Asymptotic Normality of M-estimates, 8 pages. (PDF)
3.7 Efficiency of Estimators, 11 pages. (PDF)
3.8 Efficiency of Maximum Likelihood Estimators, 4 pages. (PDF)
3.9 A Likelihood Ratio Test for Nested Composite Hypotheses: Wilks's theorem, 5 pages. (PDF)


Chapter 4: Asymptotics of Posterior Probabilities and Model Selection

4.1 Convergence of Posteriors, 5 pages. (PDF)


Appendices

Appendix A. Uniqueness of Likelihood Ratios, 2 pages. (PDF)
Appendix B. Preservation of Dimension by 1-1 Continuous Functions, 1 page. (PDF)
Appendix C. Separability of Stochastic Processes, 1 page. (PDF)
Appendix D. Mathematical Foundations of Probability Theory, 2 pages. (PDF)
Appendix E. Line-fitting by Distance: Errors-in-variables Regression, 3 pages. (PDF)
Appendix F. The Lagrange Multiplier Technique, 2 pages. (PDF)


*Note: Starred (*) sections such as 1.4* and 2.8* are not used later in the text and can be omitted on first reading.


 








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