1. Probability Theory.
Set Theory. Probability Theory. Conditional Probability and
Independence. Random Variables. Distribution Functions. Density and
Mass Functions. Exercises. Miscellanea.
2. Transformations and Expectations.
Distribution of Functions of a Random Variable. Expected Values.
Moments and Moment Generating Functions. Differentiating Under an
Integral Sign. Exercises. Miscellanea.
3. Common Families of Distributions.
Introductions. Discrete Distributions. Continuous Distributions.
Exponential Families. Locations and Scale Families. Inequalities
and Identities. Exercises. Miscellanea.
4. Multiple Random Variables.
Joint and Marginal Distributions. Conditional Distributions and
Independence. Bivariate Transformations. Hierarchical Models and
Mixture Distributions. Covariance and Correlation. Multivariate
Distributions. Inequalities. Exercises. Miscellanea.
5. Properties of a Random Sample.
Basic Concepts of Random Samples. Sums of Random Variables from a
Random Sample. Sampling for the Normal Distribution. Order
Statistics. Convergence Concepts. Generating a Random Sample.
Exercises. Miscellanea.
6. Principles of Data Reduction.
Introduction. The Sufficiency Principle. The Likelihood Principle.
The Equivariance Principle. Exercises. Miscellanea.
7. Point Estimation.
Introduction. Methods of Finding Estimators. Methods of Evaluating
Estimators. Exercises. Miscellanea.
8. Hypothesis Testing.
Introduction. Methods of Finding Tests. Methods of Evaluating Test.
Exercises. Miscellanea.
9. Interval Estimation.
Introduction. Methods of Finding Interval Estimators. Methods of
Evaluating Interval Estimators. Exercises. Miscellanea.
10. Asymptotic Evaluations.
Point Estimation. Robustness. Hypothesis Testing. Interval
Estimation. Exercises. Miscellanea.
11. Analysis of Variance and Regression.
Introduction. One-way Analysis of Variance. Simple Linear
Regression. Exercises. Miscellanea.
12. Regression Models.
Introduction. Regression with Errors in Variables. Logistic
Regression. Robust Regression. Exercises. Miscellanea. Appendix.
Computer Algebra. References.
"Statistical Inference is a delightfully modern text on statistical theory and deserves serious consideration from every teacher of a graduate- or advanced undergraduate-level first course in statistical theory. . . Chapters 1-5 provide plenty of interesting examples illustrating either the basic concepts of probability or the basic techniques of finding distribution. . . The book has unique features [throughout Chapters 6-12] for example, I have never seen in any comparable text such extensive discussion of ancillary statistics [Ch. 6], including Basu's theorem, dealing with the independence of complete sufficient statistics and ancillary statistics. Basu's theorem is such a useful tool that it should be available to every graduate student of statistics. . . The derivation of the analysis of variance (ANOVA)F test in Chapter 11 via the union-intersection principle is very nice. . . Chapter 12 contains, in addition to the standard regression model, errors-in-variables models. This topic will be of considerable importance in the years ahead, and the authors should be thanked for giving the reader an introduction to it. . . Another nice feature is the Miscellanea Section at the end of nearly every chapter. This gives the serious student an opportunity to go beyond the basic material of the text and look at some of the more advanced work on the topics, thereby developing a much better feel for the subject."
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