Theoretical Statistics: Topics for a Core CourseIntended as the text for a sequence of advanced courses, this book covers major topics in theoretical statistics in a concise and rigorous fashion. The discussion assumes a background in advanced calculus, linear algebra, probability, and some analysis and topology. Measure theory is used, but the notation and basic results needed are presented in an initial chapter on probability, so prior knowledge of these topics is not essential. |
Contents
1 | |
2 Exponential Families | 25 |
3 Risk Sufficiency Completeness and Ancillarity | 39 |
4 Unbiased Estimation | 61 |
5 Curved Exponential Families | 85 |
6 Conditional Distributions | 101 |
7 Bayesian Estimation | 115 |
8 LargeSample Theory | 129 |
14 General Linear Model | 269 |
Modeling andComputation | 301 |
16 Asymptotic Optimality1 | 319 |
17 LargeSample Theory for Likelihood RatioTests | 343 |
18 Nonparametric Regression | 367 |
19 Bootstrap Methods | 391 |
20 Sequential Methods | 405 |
A Appendices | 431 |
9 Estimating Equations and Maximum Likelihood | 151 |
10 Equivariant Estimation | 195 |
11 Empirical Bayes and Shrinkage Estimators | 205 |
12 Hypothesis Testing | 219 |
13 Optimal Tests in Higher Dimensions | 254 |
B Solutions | 450 |
525 | |
530 | |