Preface
1 Probability and Distributio
1．1 Introduction
1．2 Set Theory
1．3 The Probability Set Function
1．4 Conditional Probability and Independence
1．5 Random Variables
1．6 Discrete Random Variables
1．6．1 naformatio
1．7 Continuous Random Variables
1．7．1 naDSformatio
1．8 Expectation of a Random Variable
1．9 Some Special Expectatio
1．10 Important Inequalities
2 Multivariate Distributio
2．1 Distributio of Two Random Variables
2．1．1Expectation
2．2 naformatio：Bivariate Random Variables
2．3 Conditional Distributio and Expectatio
2．4 The Correlation Coefficient
2．5 Independent Random Variables
2．6 Exteion to Several Random Variables
2．6．1*Multivariate Variance-Covariance Matrix
2．7 naformatio for Several Random Variables
2．8 Linear Combinatio of Random Variables
3 Some Special Distributio
3．1 The Binomial and Related Distributio
3．2 The Poisson Distribution
3．3 The Г，χ2，andβ Distributio
3．4 The Normal Distribution
3．4．1Contaminated Normals
3．5 The Multivariate Normal Distribution
3．5．1*Applicatio
3．6 t-and F-Distributio
3．6．1 The t-distribution
3．6．2 The F-distribution
3．6．3 Student’S Theorem
3．7 Mixture Distributio
4 Some Elementary Statistical Inferences
4．1 Sampling and Statistics
4．1．1 Histogram Estimates of pmfs and pdfs
4．2 Confidence Intervals
4．2．1Confidence Intervals for Difference in Mea
4．2．2Confidence Interval for Difference in Proportio
4．3 Confidence Intervals for Paramete of Discrete Distributio
4．4 CIrder Statistics
4．4．1Quantiles
4．4．2Confidence Intervals for Quantiles
4．5 Introduction to Hypothesis Testing
4．6 Additional Comments About Statistical Tests
4．7 Chi-Square Tests
4．8 The Method of Monte Carlo
4．8．1 Accept-Reject Generation Algorithm
4．9 Bootstrap Procedures
4．9．1 Percentile Bootstrap Confidence Intervals
4．9．2Bootstrap Testing Procedures
4．10 *Tolerance Limits for Distributio
5 Coistency and Limiting Distributio
5．1 Convergence in Probability
5．2 Convergence in Distribution
5．2．1Bounded in Probability
5．2．2 △-Method
5．2．3 Moment Generating Function Technique
5．3 Central Limit Theorem
5．4 *Exteio to Multivariate Distributio
6 Maximum Likelihood Methods
6．1 Maximum Likeli．hood Estimation
6．2 Rao-Cram6r Lower Bound and E伍ciency
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 Estimato
7．2 A Su伍cient Statistic for a Parameter
7．3 Properties of a Sufficient Statistic
7．4 Completeness and Uniqueness
7．5 The Exponential Class of Distributio
7．6 Functio of a Parameter
7．7 The Cuse of Several Paramete
7．8 Minimal Sufficiency and Ancillary Statistics
7．9 Sufficiency,Completeness．and Independence
8 Optimal Tests of Hypotheses
8．1 Most Powerful Tests
8．2 Uniformly Most Powerful Tests
8．3 Likelihood Ratio Tests
8．4 The Sequential Probability Ratio Test
8．5Minimax and Classification Procedures
8．5．1 Minimax Procedures
8．5．2 Classification
9 Inferences About Normal MOdels
9．1 Quadratic Forms
9．2 One-Way ANOVA
9．3 Noncentralχ2and F-Distributio
9．4 Multiple Compariso
9．5 The Analysis of Variance
9．6 A Regression Problem
9．7 A Test of Independence
9．8 The Distributio of Certain Quadratic Forms
9．9 The Independence of Certain Quadratic Forills
10 Nonparametric and Robust Statistics
10．1 Location Models
10．2 Sample Median and the Sign Test
10．2．1 Asymptotic Relative Efficiency
10．2．2 Estimating Equatio Based on the Sign Test
10．2．3 Confidence Interval for the Median
10．3 Signed-Rank Wilcoxon
10．3．1 Asymptotic Relative Emciency
10．3．2 Estimating Equatio Based on Signed-Rank Wilcoxon
10．3．3 Confidence Interval for the Median
10．4 Mann-Whitnev-Wilcoxon Procedure
10．4．1 Asymptotic Relative Efficiency
10．4．2 Estimating Equatio Based on the Mann-Whitney-Wilcoxon
10．4．3 Confidence Interval for the Shift Parameter △
10．5 General Rank Scores
10．5．1 Efficacy
10．5．2 Estimating Equatio Based on General Scores
10．5．3 0ptimization：Best Estimates
10．6 Adaptive Procedures
10．7 Simple Linear Model
10．8 Measures of Association
10．8．1 Kendall’S т
10．8．2 Spearman’S Rho
10．9 Robust Concepts
10．9．1 Location Model
10．9．2 Linear Model
11 Bayesian Statistics
11．1 Subjective Probability
11．2 Bayesian Procedures
11．2．1 Prior and Posterior Distributio
11．2．2 Bayesian Point Estimation
11．2．3 Bayesian Interval Estimation
11．2．4 Bayesian Testing Procedures
11．2．5 Bayesian Sequential Procedures
11．3 More Bayesian Terminology and Ideas
11．4 Gibbs Sampler
11．5 Modern Bayesian Methods
11．5．1 Empirical Bayes
A Mathematical Comments
A．1 Regularity Conditio
A．2 Sequences
B R Functio
C Tables of Distributio
D Lists of Common Distributio
E References
F Awe to Selected Exercisds
Index
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