《基於Copula的相關測度》是2020年經濟管理出版社出版的圖書。
基本介紹
- 中文名：基於Copula的相關測度
- 作者：單青松
- 出版社：經濟管理出版社
- 出版時間：2020年
- 開本：16 開
- 裝幀：平裝
- ISBN：9787509661871
內容簡介,作者簡介,圖書目錄,
內容簡介
Copula 在套用統計領域，如金融、氣象、水文等有廣泛的套用。本書從copula視角介紹了變數間幾種相關性的度量，著重討論了變數之間函式型關係強弱的基於copula的度量。
變數間的函式型關係是一種較為廣泛的概念，既包括了常見的線性關係、非線性單調關係，也包括了目前較少討論的非單調關係。因此本文的工作具有廣泛的適用性。同時也為非線性關係的度量提供了另一種思路。函式型關係是一個比線性關係、單調型關係更廣泛的概念，本書分別針對離散型和連續型函式關係作了討論。對離散型變數構造了幾種基於subcopula的測度， 並討論了這些測度的理論性質。對連續性變數的測度，主要從非參數核密度估計入手構造了其非參數估計。討論了其漸進性質，並給出了數值模擬結果。
作者簡介
單青松，201 5年獲美國新墨西哥州立大學數理統計博士學位。現任江西財經大學統計學院講師，Journal of Nonparametric Statistfcs、Scan-dinavian Journal of Statistics審稿人。主要研究方向為非參數統計和Copula理論。
圖書目錄
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
