时代教育国外高校优秀教材精选:统计推断.pdf

时代教育国外高校优秀教材精选:统计推断.pdf
 

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雷奥奇·卡塞拉、罗杰L.贝耶编著的《统计推断(英文版原书第2版)》从概率的基础开始,并不假定任何概率论的先修知识。通过正文与习题旁征博引,引进了大量近代统计处理的新技术,及一些在国内同类教材中不常见、而广为使用的分布。例如习题中介绍了在建模中和Bayes统计中被广泛用作先验分布的逆Gamma分布、逆Gauss分布等。第1章至第4章是有关概率,如随机变量的基本知识。第5章以后的大量篇幅是讲统计,它比当前国内概率统计方向的相应课程的理论难度要低,但是与国内目前流行的非概率统计教材中的统计内容相比,理论上较深,论述的模型较多,案例的涉及面要广,理论的应用面要丰富,统计思想的阐述与算法更为具体。
本书也适合作为广大工科有关概率统计的教学参考书,以及相关领域的教师、工程师、技术人员作为自学之用。

作者简介
作者:(美)雷奥奇·卡塞拉、罗杰L.贝耶

目录
出版说明

1 Probability Theory
1.1 Set Theory
1.2 Basics of Probability Theory
1.2.1 Axiomatic Foundations
1.2.2 The Calculus of Probabilities
1.2.3 Counting
1.2.4 Enumerating Outcomes
1.3 Conditional Probability and Independence
1.4 Random Variables
1.5 Distribution Functions
1.6 Density and Mass Functions
1.7 Exercises
1.8 Miscellanea
2 Transformations and Expectations
2.1 Distributions of Functions of a Random Variable
2.2 Expected Values
2.3 Moments and Moment Generating Functions
2.4 Differentiating Under an Integral Sign
2.5 Exercises
2.6 Miscellanea
3 Common Families of Distributions
3.1 Introduction
3.2 Discrete Distributions
3.3 Continuous Distributions
3.4 Exponential Families
3.5 Location and Scale Families
3.6 Inequalities and Identities
3.6.1 Probability Inequalities
3.6.2 Identities
3.7 Exercises
3.8 Miscellanea
4 Multiple Random Variables
4.1 Joint and Marginal Distributions
4.2 Conditional Distributions and Independence
4.3 Bivariate Transformations
4.4 Hierarchical Models and Mixture Distributions
4.5 Covariance and Correlation
4.6 Multivariate Distributions
4.7 Inequalities
4.7.1 Numerical Inequalities
4.7.2 Functional Inequalities
4.8 Exercises
4.9 Miscellanea
5 Properties of a Random Sample
5.1 Basic Concepts of Random Samples
5.2 Sums of Random Variables from a Random Sample
5.3 Sampling from the Normal Distribution
5.3.1 Properties of the Sample Mean and Variance
5.3.2 The Derived Distributions: Student's t and Snedecor's F
5.4 Order Statistics
5.5 Convergence Concepts
5.5.1 Convergence in Probability
5.5.2 Almost Sure Convergence
5.5.3 Convergence in Distribution
5.5.4 The Delta Method
5.6 Generating a Random Sample
5.6.1 Direct Methods
5.6.2 Indirect Methods
5.6.3 The Accept/Reject Algorithm
5.7 Exercises
5.8 Miscellanea
6 Principles of Data Reduction
6.1 Introduction
6.2 The Sufficiency Principle
6.2.1 Sufficient Statistics
6.2.2 Minimal Sufficient Statistics
6.2.3 Ancillary Statistics
6.2.4 Sufficient, Ancillary, and Complete Statistics
6.3 The Likelihood Principle
6.3.1 The Likelihood Function
6.3.2 The Formal Likelihood Principle
6.4 The Equivariance Principle
6.5 Exercises
6.6 Miscellanea
7 Point Estimation
7.1 Introduction
7.2 Methods of Finding Estimators
7.2.1 Method of Moments
7.2.2 Maximum Likelihood Estimators
7.2.3 Bayes Estimators
7.2.4 The EM Algorithm
7.3 Methods of Evaluating Estimators
7.3.1 Mean Squared Error
7.3.2 Best Unbiased Estimators
7.3.3 Sufficiency and Unbiasedness
7.3.4 Loss Function Optimality
7.4 Exercises
7.5 Miscellanea
8 Hypothesis Testing
8.1 Introduction
8.2 Methods of Finding Tests
8.2.1 Likelihood Ratio Tests
8.2.2 Bayesian Tests
8.2.3 Union-Intersection and Intersection-Union Tests
8.3 Methods of Evaluating Tests
8.3.1 Error Probabilities and the Power Function
8.3.2 Most Powerful Tests
8.3.3 Sizes of Union-Intersection and Intersection-Union Tests
8.3.4 p-Values
8.3.5 Loss Function Optimality
8.4 Exercises
8.5 Miscellanea
9 Interval Estimation
9.1 Introduction
9.2 Methods of Finding Interval Estimators
9.2.1 Inverting a Test Statistic
9.2.2 Pivotal Quantities
9.2.3 Pivoting the CDF
9.2.4 Bayesian Intervals
9.3 Methods of Evaluating Interval Estimators
9.3.1 Size and Coverage Probability
9.3.2 Test-Related Optimality
9.3.3 Bayesian Optimality
9.3.4 Loss Function Optimality
9.4 Exercises
9.5 Miscellanea
10 Asymptotic Evaluations
10.1 Point Estimation
10.1.1 Consistency
10.1.2 Efficiency
10.1.3 Calculations and Comparisons
10.1.4 Bootstrap Standard Errors
10.2 Robustness
10.2.1 The Mean and the Median
10.2.2 M-Estimators
10.3 Hypothesis Testing
10.3.1 Asymptotic Distribution of LRTs
10.3.2 Other Large-Sample Tests
10.4 Interval Estimation
10.4.1 Approximate Maximum Likelihood Intervals
10.4.2 Other Large-Sample Intervals
10.5 Exercises
10.6 Miscellanea
11 Analysis of Variance and Regression
11.1 Introduction
11.2 0neway Analysis of Variance
11.2.1 Model and Distribution Assumptions
11.2.2 The Classic ANOVA Hypothesis
11.2.3 Inferences Regarding Linear Combinations of Means
11.2.4 The ANOVA F Test
11.2.5 Simultaneous Estimation of Contrasts
11.2.6 Partitioning Sums of Squares
11.3 Simple Linear Regression
11.3.1 Least Squares: A Mathematical Solution
11.3.2 Best Linear Unbiased Estimators: A Statistical Solution
11.3.3 Models and Distribution Assumptions
11.3.4 Estimation and Testing with Normal Errors
11.3.5 Estimation and Prediction at a Specified x -- x0
11.3.6 Simultaneous Estimation and Confidence Bands
11.4 Exercises
11.5 Miscellanea
12 Regression Models
12.1 Introduction
12.2 Regression with Errors in Variables
12.2.1 Functional and Structural Relationships
12.2.2 A Least Squares Solution
12.2.3 Maximum Likelihood Estimation
12.2.4 Confidence Sets
12.3 Logistic Regression
12.3.1 The Model
12.3.2 Estimation
12.4 Robust Regression
12.5 Exercises
12.6 Miscellanea
Appendix: Computer Algebra
Table of Common Distributions
References
Author Index
Subject Index

内容简介
雷奥奇·卡塞拉、罗杰L.贝耶编著的《统计推断(英文版原书第2版)》从概率论的基础开始,通过例子与习题的旁征博引,引进了大量近代统计处理的新技术和一些国内同类教材中不能见而广为使用的分布。其内容包括工科概率论入门、经典统计和现代统计的基础,又加进了不少近代统计中数据处理的实用方法和思想,例如:Bootstrap再抽样法、刀切(Jackknife)估计、EM算法、Logistic回归、稳健(Robust)回归、Markov链、Monte Carlo方法等。它的统计内容与国内流行的教材相比,理论较深,模型较多,案例的涉及面要广,理论的应用面要丰富,统计思想的阐述与算法更为具体。《统计推断(英文版原书第2版)》可作为工科、管理类学科专业本科生、研究生的教材或参考书,也可供教师、工程技术人员自学之用。

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