Roger Lee Berger 是美国统计学家和教授,与合作者 George Casella 于1990年首次出版《Statistical Inference》一书。
目录
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出版说明
序
1 Probability Theory
1.1 Set Theory
1.2 Basics of Probability Theory
1.2.1 Axiomatic Foundations
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出版说明
序
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
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7 Point Estimation
8 Hypothesis Testing
8.1 Introduction
9 Interval Estimation
10 Asymptotic Evaluations
11 Analysis of Variance and Regression
12 Regression Models
Appendix: Computer Algebra
Table of Common Distributions
References
Author Index
Subject Index
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If E|g(X)|=∞, we say that Eg(X) does not exist. (Ross 1988 refers to this as the "law of the unconscious statistician." We do not find this amusing.) (查看原文)
If you have basic training in calculus, you'll love this well written, easy-to-follow book. It provides a complete list of theories along with rigorous proofs and comprehensive examples, by which it is almost good for self-study. Comparing with many badly w...
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This is a classical textbook for mathematical statistics. I have to say that this book is barely ok and clearly not a perfect one as it lacks the necessary rigorous math treatment. It seems to be too easy for a student with good math background but shows ev...
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0 有用 ninainaid 2010-07-01 05:40:36
多么的便宜!
1 有用 Ryougi Shiki 2021-02-11 16:59:52
行文非常流畅的一本书,核心的理论都涉及了,深度广度兼具,习题也有答案,对于国内的概率论或者数理统计课程是非常好的一本参考和补充的书籍
0 有用 𝕯𝖊𝖓 2014-04-15 18:51:59
非常不错。给人耳目一新的感觉
1 有用 俄额俄 2015-06-15 04:33:56
难
2 有用 多情键盘无情键 2015-11-10 23:55:44
看不懂的书就一遍一遍看…说不定哪次就懂了 守着病人又看了一遍