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。
目錄：
1Outline and Summary
1.1Introduction
1.2Outline
2Statistical Modeling and Measurement of Association
2.1The concept of copulas
2.2Nonparametric estimations of copula
2.2.1An overview of empirical processes
2.2.2Nonparametric estimation via the empirical copula
2.2.3Functional delta-method and hadamard differentiability
2.2.4Weak convergence of the empirical copula process
2.2.5Nonparametric kernel estimations
2.2.6Bias and variance of kernel density estimator
2.2.7Optimal bandwith
2.3Measures of association and dependence
2.3.1Pearson''s corelation coefficient
2.3.2Spearman''s and Kendall''s
2.3.3The measure for mutual complete dependence
2.3.4The * operator and the measure of mutual complete dependence
3A Measure for Positive Quadrant Dependence
4Measures for Discrete MCD and Functional Dependence
4.1The measure of MCD through conditional distributions
4.2The measure of MCD through a subcopula
4.3Comparison to Siburg and Stoimenov''s measure of MCD
4.3.1Extension using E-process
4.3.2Bilinear extension
4.4Remarks on measures of dependence
4.5Other measures
4.5.1The measure 20
4.5.2The measure
4.5.3Construction of the measure
4.5.4Proofs of the construction of
5Nonparametric Estimation of the Measure of Functional Dependence
5.1Nonparametric estimation through the density of copula
5.1.1Estimating with pseudo-observations
5.1.2Kernel estimation through copula density functions
5.1.3Asymptotic behavior of the estimator of functional dependence
5.2Nonparametric estimation of the measure of MCD via copula
5.3Simulation results
6Implementation and Simulations
6.1Choosing the evaluation grid
6.2Simulation
6.3Comparison of measures
7Application
8Discussion
References
Appendix
AList of Symbols
BCalculation of the Measure of PQD
CBeta Kernel Estimation
DKernel Estimation
EFDM of variables in crime dataset
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