概率统计高级教程

Preface

1 An Invitation to Statistics

1.1 A Motivating Example

1.2 Generalities on Survey Sampling

1.3 Statistical Data

1.4 Statistical Models

1.5 Some Computational Statistics

1.6 Exercises

2 Sampling Distributions

2.1 Sampling from a Bernoulli Population

2.2 Sampling from a Normal Population

2.3 Sampling from an Exponential Population

2.4 Order StatisticS

2.5 Distributions of Quadratic Forms

2.6 Exercises

3 Data Reduction

3.1 Sufficient Statistics

3.2 Complete Statistics

3.3 Exponential and Location-scale Families

3.4 Exercises

4 Estimation

4.1 Point Estimation

4.2 The Best Unbiased Estimation

4.3 Fisher Information and Efficiency

4.4 Two Methods of Finding Estimators

4.5 Confidence Sets

4.6 Bayes Estimation

4.7 Exercises

5 Large Sample Estimation

5.1 Consistency

5.2 Asymptotic Normality

5.3 Asymptotic Normality of Maximum Likelihood Estimators

5.4 Asymptotic Efficiency

5.5 Large Sample Interval Estimation

5.6 Robust Estimation

5.7 Exercises

6 Tests of Statistical Hypotheses

7 Nonparametric Statistical Inference

A Common Distributions

B Some Common Statistical Tables

Bibliography

Index

· This is an update Text book for beginning graduate students in Mathematics, Probability and Statistics, Engineering, Computer Sciences, Mathematical Economics 　　
· It distinguishes from all existing texts on the subject from its pedagogical spirit, namely, motivations before mathematics; mathematics tools are only introduced when needed and motivated 　　
· All theoretical results are proved in a friendly fashion 　　
· Teaching the students, not only the concepts and possible applications, but also guiding the students with proof techniques 　　
· This series will help students to learn with full understanding and appreciation of the subject 　　
· It will provide interested students with solid background for research