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理論統(tǒng)計(jì)-第3版 版權(quán)信息
- ISBN：9787519226190
- 條形碼：9787519226190 ; 978-7-5192-2619-0
- 裝幀：一般膠版紙
- 冊(cè)數(shù)：暫無(wú)
- 重量：暫無(wú)
- 所屬分類(lèi)：>
理論統(tǒng)計(jì)-第3版 內(nèi)容簡(jiǎn)介
《理論統(tǒng)計(jì)（英文版）》是一本內(nèi)容簡(jiǎn)明，結(jié)構(gòu)嚴(yán)謹(jǐn)?shù)睦碚摻y(tǒng)計(jì)教科書(shū)，內(nèi)容包括自助法、非參數(shù)回歸、同變估計(jì)、經(jīng)驗(yàn)貝葉斯、序貫設(shè)計(jì)和分析！ 独碚摻y(tǒng)計(jì)（英文版）》各章有豐富的習(xí)題，解答在附錄中提供。讀者需具備微積分、線性代數(shù)、概率論、數(shù)學(xué)分析和拓?fù)涞葦?shù)學(xué)基礎(chǔ)知識(shí)。目次：概率和測(cè)度；指數(shù)族；風(fēng)險(xiǎn)，充分性，完整性；無(wú)偏估計(jì)；曲指數(shù)族；條件分布；貝葉斯估計(jì)；大樣本理論；估計(jì)方程和大概似值；同變估計(jì)；經(jīng)驗(yàn)貝葉斯法和收縮估計(jì)；假設(shè)檢驗(yàn)；高維優(yōu)化試驗(yàn)等。
理論統(tǒng)計(jì)-第3版 目錄
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
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
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