理论统计(第3版)
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作者Robert W. Keener[著]
出版社世界图书出版有限公司北京分公司
ISBN9787519226190
出版时间2017-08
装帧平装
开本其他
定价85元
货号9253993
上书时间2024-11-12
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目录
1 Probability and Measure
1.1 Measures
1.2 Integration
1.3 Events, Probabilities, and Random Variables
1.4 Null Sets
1.5 Densities
1.6 Expectation
1.7 Random Vectors
1.8 Covariance Matrices
1.9 Product Measures and Independence
1.10 Conditional Distributions
1.11 Problems
2 Exponential Families
2.1 Densities and Parameters
2.2 Differential Identities
2.3 Dominated Convergence
2.4 Moments, Cumulants, and Generating Functions
2.5 Problems
3 Risk, Sufficiency, Completeness, and Ancillarity
3.1 Models, Estimators, and Risk Functions
3.2 Sufficient Statistics
3.3 Factorization Theorem
3.4 Minimal Sufficiency
3.5 Completeness
3.6 Convex Loss and the Rao-Blackwell Theorem
3.7 Problems
4 Unbiased Estimation
4.1 Minimum Variance Unbiased Estimators
4.2 Second Thoughts About Bias
4.3 Normal One-Sample Problem--Distribution Theory
4.4 Normal One-Sample Problem--Estimation
4.5 Variance Bounds and Information
4.6 Variance Bounds in Higher Dimensions
4.7 Problems
5 Curved Exponential Families
5.1 Constrained Families
5.2 Sequential Experiments
5.3 Multinomial Distribution and Contingency Tables
5.4 Problems
6 Conditional Distributions
6.1 Joint and Marginal Densities
6.2 Conditional Distributions
6.3 Building Models
6.4 Proof of the Factorization Theorem
6.5 Problems
7 Bayesian Estimation
7.1 Bayesian Models and the Main Result
7.2 Examples
7.3 Utility Theory
7.4 Problems
8 Large-Sample Theory
8.1 Convergence in Probability
8.2 Convergence in Distribution
8.3 Maximum Likelihood Estimation
8.4 Medians and Percentiles
8.5 Asymptotic Relative Efficiency
8.6 Scales of Magnitude
8.7 Almost Sure Convergence
8.8 Problems
9 Estimating Equations and Maximum Likelihood
9.1 Weak Law for Random Functions
9.2 Consistency of the Maximum Likelihood Estimator
9.3 Limiting Distribution for the MLE
9.4 Confidence Intervals
9.5 Asymptotic Confidence Intervals
9.6 EM Algorithm: Estimation from Incomplete Data
9.7 Limiting Distributions in Higher Dimensions
9.8 M-Estimators for a Location Parameter
9.9 Models with Dependent Observations
9.10 Problems
10 Equivariant Estimation
10.1 Group Structure
10.2 Estimation
10.3 Problems
11 Empirical Bayes and Shrinkage Estimators
11.1 Empirical Bayes Estimation
11.2 Risk of the James-Stein Estimator
11.3 Decision Theory
11.4 Problems
12 Hypothesis Testing
12.1 Test Functions, Power, and Significance
12.2 Simple Versus Simple Testing
12.3 Uniformly Most Powerful Tests
12.4 Duality Between Testing and Interval Estimation
12.5 Generalized Neyman-Pearson Lemma
12.6 Two-Sided Hypotheses
12.7 Unbiased Tests
12.8 Problems
13 Optimal Tests in Higher Dimensions
13.1 Marginal and Conditional Distributions
13.2 UMP Unbiased Tests in Higher Dimensions
13.3 Examples
13.4 Problems
14 General Linear Model
14.1 Canonical Form
14.2 Estimation
14.3 Gauss-Markov Theorem
14.4 Estimating σ2
14.5 Simple Linear Regression
14.6 Noncentral F and Chi-Square Distributions
14.7 Testing in the General Linear Model
14.8 Simultaneous Confidence Intervals
14.9 Problems
15 Bayesian Inference: Modeling and Computation
15.1 Hierarchical Models
15.2 Bayesian Robustness
15.3 Markov Chains
15.4 Metropolis-Hastings Algorithm
15.5 Gibbs Sampler
15.6 Image Restoration
15.7 Problems
16 Asymptotic Optimality
16.1 Superefficiency
16.2 Contiguity
16.3 Local Asymptotic Normality
16.4 Minimax Estimation of a Normal Mean
16.5 Posterior Distributions
16.6 Locally Asymptotically Minimax Estimation
16.7 Problems
17 Large-Sample Theory for Likelihood Ratio Tests
17.1 Generalized Likelihood Ratio Tests
17.2 Asymptotic Distribution of 2 log A
17.3 Examples
17.4 Wald and Score Tests
17.5 Problems
18 Nonparametric Regression
18.1 Kernel Methods
18.2 Hilbert Spaces
18.3 Splines
18.4 Density Estimation
18.5 Problems
19 Bootstrap Methods
19.1 Introduction
19.2 Bias Reduction
19.3 Parametric Bootstrap Confidence Intervals
19.4 Nonparametric Accuracy for Averages
19.5 Problems
20 Sequential Methods
20.1 Fixed Width Confidence Intervals
20.2 Stopping Times and Likelihoods
20.3 Optimal Stopping
20.4 Sequential Probability Ratio Test
20.5 Sequential Design
20.6 Problems
A Appendices
A.1 Functions
A.2 Topology and Continuity in Rn
A.3 Vector Spaces and the Geometry of Rn
A.4 Manifolds and Tangent Spaces
A.5 Taylor Expansion for Functions of Several Variables
A.6 Inverting a Partitioned Matrix
A.7 Central Limit Theory
A.7.1 Characteristic Functions
A.7.2 Central Limit Theorem
A.7.3 Extensions
B Solutions
B.1 Problems of Chapter 1
B.2 Problems of Chapter 2
B.3 Problems of Chapter 3
B.4 Problems of Chapter 4
B.5 Problems of Chapter 5
B.6 Problems of Chapter 6
B.7 Problems of Chapter 7
B.8 Problems of Chapter 8
B.9 Problems of Chapter 9
B.10 Problems of Chapter 10
B.11 Problems of Chapter 11
B.12 Problems of Chapter 12
B.13 Problems of Chapter 13
B.14 Problems of Chapter 14
B.17 Problems of Chapter 17
References
Index
精彩内容
R.W.基纳著的《理论统计(英文版)》是一本内容简明，结构严谨的理论统计教科书，内容包括自助法、非参数回归、同变估计、经验贝叶斯、序贯设计和分析。本书各章有丰富的习题，解答在附录中提供。读者需具备微积分、线性代数、概率论、数学分析和拓扑等数学基础知识。目次：概率和测度；指数族；风险，充分性，完整性；无偏估计；曲指数族；条件分布；贝叶斯估计；大样本理论；估计方程和最大概似值；同变估计；经验贝叶斯法和收缩估计；假设检验；高维优化试验等。
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