Jin Zhang编著的《数理统计》内容介绍：This book grew from my
lecture notes developed for teaching mathematicalstatistics at
Yunnan University China and University of Manitoba Canada.
Thecontents and structure of the book are mainly taken from the
classical textbookMathematical Statistics: Basic Ideas and Selected
Topics Vol I, 2nd ed. PrenticeHall, 2002 by P. J. Bickel and K.
A. Doksum, with reference to other standardtextbooks, such as
Mathematical Statistics by K.Knight, Statistical Inference 2nd ed.
Duxbury Press, 2002 by G. Casella and R.L. Berger, and
Introduction to Mathematical Statistics 6th ed. Prentice Hall,
2005by R. V. Hogg, J. W. Mckean and A. T. Craig. The mathematical
background necessary for this book is linear algebra andadvance
calculus but no measure theory. It is assumed that the reader is
familiarwith basic probability theory and statistical
principle.
目錄：
1 Statistical Models and Principles
1.1 Statistical Models
1.1.1 Data and Models
1.1.2 Parameters and Statistics
1.2 Bayesian Models
1.3 The Framework of Decision Theory
1.3.1 Components of the Decision Theory
1.3.2 Bayes and Minimax Criteria
1.4 Prediction
1.5 Sufficiency
1.6 Exponential Families
1.6.1 The One-Parameter Case
1.6.2 The Multiparameter Case
1.6.3 Properties of Exponential Families
1.6.4 Conjugate Families of Prior
Distributions
1.7 Exercises
2 Methods of Parameter Estimation
2.1 Essentials of Point Estimation
2.1.1 M-Estimation
2.1.2 The Substitution Principle
2.2 Least Squares and Maximum Likelihood
Methods
2.2.1 Least Squares and Weighted Least
Squares Estimation
2.2.2 Maximum Likelihood Estimation
2.3 The MLE in Exponential Families
2.4 Algorithmic Issues for Parameter Estimation
2.4.1 The Bisection Method
2.4.2 The Coordinate Ascent Method
2.4.3 The Newton-Raphson Algorithm
2.4.4 The EM Algorithm
2.5 Exercises
3 Measures of Performance and Optimality
3.1 Bayes Principle
3.2 Minimax Principle
3.3 Unbiased Estimation
3.4 The Information Inequality
3.4.1 The One-Parameter Case
3.4.2 The Multiparameter Case
3.5 Exercises
4 Hypothesis Tests and Confidence Regions
4.1 The Framework of Hypothesis Testing
4.2 The Neyman-Pearson Test
4.3 Uniformly Most Powerful Tests
4.4 Confidence Intervals and Regions
4.5 The Duality between Confidence Regions and
Hypothesis Tests
4.6 Uniformly Most Accurate Confidence Bounds
4.7 Bayesian Formulation of Credible Regions
4.8 Prediction Intervals
4.9 Likelihood Ratio Tests
4.9.1 Introduction
4.9.2 One-Sample Problem for a Normal
Distribution
4.9.3 Two-Sample Problem with Equal
Variance
4.9.4 Two-Sample Problem with Unequal
Variances
4.9.5 Likelihood Ratio Tests for Bivariate
Normal Distributions
4.10 Exercises
5 Asymptotic Theories
5.1 Introduction
5.2 Consistency
5.2.1 Consistency in Estimation
5.2.2 Consistency of M-Estimates
5.3 Asymptotics Based on the Delta Method
5.3.1 The Delta Method for Approximations of
Moments
5.3.2 The Delta Method for Approximations of
Distributions
5.4 Asymptotic Theory in One Dimension
5.4.1 Asymptotic Normality of
M-Estimates
5.4.2 Asymptotic Normality and Efficiency of
MLEs
5.4.3 One-Sided Tests and Confidence
Intervals Based on the MLE
5.5 Asymptotic Theory of the Posterior
Distribution
5.6 Exercises
6 Asymptotics in the Multiparameter Case
6.1 Asymptotic Normality in k Dimensions
6.1.1 Asymptotic Normality of
M-Estimates
6.1.2 Asymptotic Normality and Efficiency of
MLEs
6.2 Large-Sample Tests and Confidence Regions
6.2.1 Asymptotic Distribution of the
Likelihood-Ratio Test Statistic
6.2.2 Wald''s and Rao''s Large-Sample Tests
and Confidence Regions
6.3 Large-Sample Tests for Categorical Data
6.3.1 Goodness-of-Fit Tests for Multinomial
Models
6.3.2 Goodness-of-Fit Tests for Composite
Multinomial Models
6.3.3 The X2 Tests for Contingency
Tables
6.4 Exercises
Appendix A: Table of Common Distributions.
Appendix B: Statistical Tables
Table 1. The Standard Normal Distribution
Table 2. Distribution of t
Table 3. Distribution of X2
Table 4. Distribution of F
References
Index
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