· 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
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
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