书籍详情
基于copula的相关性测度
作者：单青松
出版社：经济管理出版社
出版时间：2020-10-01
ISBN：9787509661871
定价：¥68.00
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内容简介
Copula 在应用统计领域，如金融、气象、水文等有广泛的应用。本书从copula视角介绍了变量间几种相关性的度量，着重讨论了变量之间函数型关系强弱的基于copula的度量。 变量间的函数型关系是一种较为广泛的概念，既包括了常见的线性关系、非线性单调关系，也包括了目前较少讨论的非单调关系。因此本文的工作具有广泛的适用性。同时也为非线性关系的度量提供了另一种思路。函数型关系是一个比线性关系、单调型关系更广泛的概念，本书分别针对离散型和连续型函数关系作了讨论。对离散型变量构造了几种基于subcopula的测度， 并讨论了这些测度的理论性质。对连续性变量的测度，主要从非参数核密度估计入手构造了其非参数估计。讨论了其渐进性质，并给出了数值模拟结果。
作者简介
单青松，201 5年获美国新墨西哥州立大学数理统计博士学位。现任江西财经大学统计学院讲师，Journal of Nonparametric Statistfcs、Scan-dinavian Journal of Statistics审稿人。主要研究方向为非参数统计和Copula理论。
目录
1 Outline and Summary
1.1 Introduction
1.2 Outline
2 Statistical Modeling and Measurement of Association
2.1 The concept of copulas
2.2 Nonparametric estimations of copula
2.2.1 An overview of empirical processes
2.2.2 Nonparametric estimation via the empirical copula
2.2.3 Functional delta-method and hadamard differentiability
2.2.4 Weak convergence of the empirical copula process
2.2.5 Nonparametric kernel estimations
2.2.6 Bias and variance of kernel density estimator
2.2.7 Optimal bandwith
2.3 Measures of association and dependence
2.3.1 Pearson's corelation coefficient
2.3.2 Spearman's ρ and Kendall's τ
2.3.3 The measure for mutual complete dependence
2.3.4 The * operator and the measure of mutual complete dependence
3 A Measure for Positive Quadrant Dependence
4 Measures for Discrete MCD and Functional Dependence
4.1 The measure of MCD through conditional distributions
4.2 The measure of MCD through a subcopula
4.3 Comparison to Siburg and Stoimenov's measure of MCD
4.3.1 Extension using E-process
4.3.2 Bilinear extension
4.4 Remarks on measures of dependence
4.5 Other measures
4.5.1 The measure μ20
4.5.2 The measure λ
4.5.3 Construction of the measure
4.5.4 Proofs of the construction of λ
5 Nonparametric Estimation of the Measure of Functional Dependence
5.1 Nonparametric estimation through the density of copula
5.1.1 Estimating with pseudo-observations
5.1.2 Kernel estimation through copula density functions
5.1.3 Asymptotic behavior of the estimator of functional dependence
5.2 Nonparametric estimation of the measure of MCD via copula
5.3 Simulation results
6 Implementation and Simulations
6.1 Choosing the evaluation grid
6.2 Simulation
6.3 Comparison of measures
7 Application
8 Discussion
References
Appendix
A List of Symbols
B Calculation of the Measure of PQD
C Beta Kernel Estimation
D Kernel Estimation
E FDM of variables in crime dataset
1.1 Introduction
1.2 Outline
2 Statistical Modeling and Measurement of Association
2.1 The concept of copulas
2.2 Nonparametric estimations of copula
2.2.1 An overview of empirical processes
2.2.2 Nonparametric estimation via the empirical copula
2.2.3 Functional delta-method and hadamard differentiability
2.2.4 Weak convergence of the empirical copula process
2.2.5 Nonparametric kernel estimations
2.2.6 Bias and variance of kernel density estimator
2.2.7 Optimal bandwith
2.3 Measures of association and dependence
2.3.1 Pearson's corelation coefficient
2.3.2 Spearman's ρ and Kendall's τ
2.3.3 The measure for mutual complete dependence
2.3.4 The * operator and the measure of mutual complete dependence
3 A Measure for Positive Quadrant Dependence
4 Measures for Discrete MCD and Functional Dependence
4.1 The measure of MCD through conditional distributions
4.2 The measure of MCD through a subcopula
4.3 Comparison to Siburg and Stoimenov's measure of MCD
4.3.1 Extension using E-process
4.3.2 Bilinear extension
4.4 Remarks on measures of dependence
4.5 Other measures
4.5.1 The measure μ20
4.5.2 The measure λ
4.5.3 Construction of the measure
4.5.4 Proofs of the construction of λ
5 Nonparametric Estimation of the Measure of Functional Dependence
5.1 Nonparametric estimation through the density of copula
5.1.1 Estimating with pseudo-observations
5.1.2 Kernel estimation through copula density functions
5.1.3 Asymptotic behavior of the estimator of functional dependence
5.2 Nonparametric estimation of the measure of MCD via copula
5.3 Simulation results
6 Implementation and Simulations
6.1 Choosing the evaluation grid
6.2 Simulation
6.3 Comparison of measures
7 Application
8 Discussion
References
Appendix
A List of Symbols
B Calculation of the Measure of PQD
C Beta Kernel Estimation
D Kernel Estimation
E FDM of variables in crime dataset
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