概率统计高级教程.第2卷,统计学基础(英文版)

2.6 Exercises
3 Data Reduction
3.1 Sufficient Statistics
3.2 Complete Statistics
3.3 Exponential and Location-scale Families
3.3.1 Exponential families
3.3.2 Location and scale families
3.4 Exercises
4 Estimation
4.1 Point Estimation
4.2 The Best Unbiased Estimation
4.3 Fisher Information and Efficiency
4.3.1 Fisher information
4.3.2 Cramer-Rao lower bound
4.4 Two Methods of Finding Estimators
4.4.1 The method of moments
4.4.2 The method of maximum likelihood
4.4.3 Some properties of maximum likelihood estimators
4.5 Confidence Sets
4.5.1 Pivotal quantities
4.5.2 Lengths of confidence intervals
4.6 Bayes Estimation
4.6.1 Prior and posterior distributions
4.6.2 Bayes rules and minimax rules
4.6.3 Bayes and minimax estimators
4.6.4 Bayes intervals
4.7 Exercises
Large Sample Estimation
5.1 Consistency
5.1.1 Consistent estimators
5.1.2 Consistency of sample quartiles
5.1.3 Consistency of maximum likelihood estimators
5.2 Asymptotic Normality
5.2.1 Univariate asymptotic distributions
5.2.2 The Delta method
5.2.3 Asymptotic distributions of the sample quartiles
5.2.4 Multivariate asymptotic distributions
5.3 Asymptotic Normality of Maximum Likelihood Estimators
5.4 Asymptotic Efficiency
5.5 Large Sample Interval Estimation
5.5.1 Asymptotically pivotal quantities
5.5.2 Intervals based on maximum likelihood estimators
5.6 Robust Estimation
5.6.1 The influence function
5.6.2 L-estimators
5.6.3 M-estimators
5.7 Exercises
Tests of Statistical Hypotheses ..
6.1 Introduction
6.2 Basic Concepts in Hypothesis Testing
6.2.1 Two hypotheses
6.2.2 Two types of errors and the power function
6.2.3 The p-value
6.2.4 Randomized tests
6.3 Most Powerful Tests
6.3.1 Neyman-Pearson lemma
6.4 Uniformly Most Powerful Tests
6.4.1 Uniformly most powerful tests
6.4.2 Monotone likelihood ratio
6.4.3 Tests in one-parameter exponential family
6.5 Unbiased Tests
6.6 Tests and Confidence Sets
6.7 Likelihood Ratio Tests . .
6.7.1 Likelihood ratio tests
6.7.2 Asymptotic distribution of the likelihood ratio
6.8 Sequential Probability Ratio Tests
6.9 Chi-Square Tests
6.9.1 Goodness-of-fit tests
6.9.2 Tests in contingency tables
6.10 Bayes Tests
6.11 Summary of Tests for Normal Populations
6.11.1 One sample test procedures
6.11.2 Two-sample test procedures
6.11.3 Tests in Bernoulli models for large samples
6.11.4 The paired t-test
6.12 Exercises
Nonparametric Statistical Inference
7.1 Inferences on Quartiles
7.1.1 Confidence intervals for quartiles
7.1.2 The sign test
7.1.3 Asymptotic relative efficiency
7.2 The Wilcoxon Signed Rank Test
7.3 The Mann-Whitney-Wilcoxon Test
7.4 The Kolmogorov-Smirnov Test and Test of' Normality
7.4.1 The Kolmogorov-Smirnov Test
7.4.2 Two-sample Kolmogorov-Smirnov test
7.4.3 Test of normality
7.5 Exercises
Appendices
A Common Distributions
A.1 Univariate Discrete Distributions
A.2 Univariate Continuous Distributions
A.3 Multivariate Distributions
B Some Common Statistical Tables
B.1 The Standard Normal Distribution
B.2 The Student's t Distribution
B.3 The chi-Square Distribution
B.4 The F Distribution
Bibliography
Index ...