Copies of the classnotes are on the internet in PDF format as given below. The notes and supplements may contain hyperlinks to posted webpages; the links appear in red fonts. The "Proofs of Theorems" files were prepared in Beamer. The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses. These notes have not been classroom tested and may have typographical errors.

The catalog description for Mathematical Statistics 1 is: "An introduction to the theory of probability and mathematical statistics. Topics will include discrete and continuous probability distributions and their applications, mathematical expectation and moment generating functions, functions of random variables and transformations, sampling distributions, the central limit theorem, χ-square, t and F distributions." The prerequisites are Linear Algebra (MATH 2010), Foundations of Probability and Statistics - Calculus Based (MATH 2050), and Calculus 3 (MATH 2110). Notice that Mathematical Statistics 1 is a sufficient prerequisite for Mathematical Statistics 2 (STAT 4057/5057), Applications of Statistics (STAT 4287/5287), and Sampling and Survey Techniques (STAT 4307/5307). More details about Mathematical Statistics 1 are on my Mathematical Statistics 1 - Class Notes webpage.

Mathematical Statistics 2 deals more with the statistical concepts and the catalog description for it is: "A continuation of Mathematical Statistics I. An introduction to the theory of mathematical statistics, estimation, and hypothesis testing. Topics will include efficiency, consistency, sufficiency, robustness, methods of estimation, confidence intervals, Bayesian inference as well as the Neyman-Pearson lemma, power functions, likelihood ratio tests, hypothesis tests, and applications." These descriptions are based on the ETSU 2019-20 Undergraduate Catalog.

Author Joseph McKean has a HOMEPAGE for the 8th EDITION of HMC where auxillary and supplemental material (including information on the software R) for the book can be downloaded. In particular, there is a Mathematical Primer for the 8th Edition which covers some topics from calculus and analysis (the topic of multiple integration is central to this class) and an Errata Sheet for the 8th Edition.

4. Some Elementary Statistical Inference.

• 4.1. Sampling and Statistics. Section 4.1 notes
• 4.2. Confidence Intervals. Section 4.2 notes
• Supplement. Examples, Exercises, and Proofs from Section 4.2. Beamer file of Section 4.2 examples and proofs (prepared in Beamer).
• Supplement. Printouts of Examples, Exercises, and Proofs from Section 4.2. Print file of Section 4.2 examples and proofs
• 4.3. Confidence Intervals for Parameters of Discrete Distributions. Section 4.3 notes (Includes an application of the Bisection Method.)
• Supplement. Examples, Exercises, and Proofs from Section 4.3. Beamer file of Section 4.3 examples and proofs (prepared in Beamer).
• Supplement. Printouts of Examples, Exercises, and Proofs from Section 4.3. Print file of Section 4.3 examples and proofs
• 4.4. Order Statistics. (partial) Section 4.4 notes
• 4.5. Introduction to Hypothesis Testing. (partial) Section 4.5 notes
• 4.6. Additional Comments About Statistical Tests.
• 4.7. Chi-Square Tests.
• 4.8. The Method of Monte Carlo.
• 4.9. Bootstrap Procedures.
• 4.10. Tolerance Limits for Distributions.

6. Maximum Likelihood Methods.

• 6.1. Maximum Likelihood Estimation.
• 6.2. Rao-Cramer Lower Bound and Efficiency.
• 6.3. Maximum Likelihood Tests.
• 6.4. Multiparameter Case: Estimation.
• 6.5. Multiparameter Case: Testing.
• 6.6. The EM Algorithm.

7. Sufficiency

• 7.1. Measures of Quality of Estimators.
• 7.2. A Sufficient Statistic for a Parameter.
• 7.3. Properties of a Sufficient Statistic.
• 7.4. Completeness and Uniqueness.
• 7.5. The Exponential Class of Distributions.
• 7.6. Functions of a Parameter.
• 7.7. The Case of Several Parameters.
• 7.8. Minimal Sufficiency and Ancillary Statistics.
• 7.9. Sufficiency, Completeness, and Independence.

8. Optimal Tests of Hypotheses.

• 8.1. Most Powerful Tests. (This section includes the Neyman-Pearson Theorem.)
• 8.2. Uniformly Most Powerful Tests.
• 8.3. Likelihood Ratio Tests.
• 8.4. The Sequential Probability Ratio Test.
• 8.5. Minimax and Classification Procedures.

9. Inferences About Normal Linear Models.

• 9.1. Introduction.
• 9.2. One-Way ANOVA.
• 9.3. Noncentral χ² and F-Distributions.
• 9.4. Multiple Comparisons.
• 9.5. Two-Way ANOVA.
• 9.6. A Regression Problem.
• 9.7. A Test of Independence.
• 9.8. The Distributions of Certain Quadratic Forms.
• 9.9. The Independence of Certain Quadratic Forms.

10. Nonparametric and Robust Statistics.

• 10.1. Location Models.
• 10.2. Sample Median and the Sign Test.
• 10.3. Signed-Rank Wilcoxon.
• 10.4. Mann-Whitney-Wilcoxon Procedure.
• 10.5. General Rank Scores.
• 10.6. Adaptive Procedures.
• 10.7. Simple Linear Model.
• 10.8. Measures of Association.
• 10.9. Robust Concepts.

11. Bayesian Statistics.

• 11.1. Bayesian Procedures.
• 11.2. More Bayesian Terminology and Ideas.
• 11.3. Gibbs Sampler.
• 11.4. Modern Bayesian Methods.

Appendices.

• Chapter 1. Probability and Distributions.
• Chapter 2. Multivariate Distributions.
• Chapter 3. Some Special Distributions.
• Chapter 5. Consistency and Limiting Distributions.
• Appendix A. Mathematical Comments.
• Appendix B. R Primer.
• Appendix C. List of Common Distributions.
• Appendix D. Tables of Distributions.
• Appendix E. References.

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