基于copula的相关性测度
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广东广州
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作者单青松
出版社经济管理出版社
ISBN9787509661871
出版时间2020-10
装帧平装
开本16开
定价68元
货号29118338
上书时间2024-10-29
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导语摘要
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
目录
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
内容摘要
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。
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