Kendall's tau and Spearman's rho forn-dimensional Archimedean copulas and their asymptotic properties
| Autor: | Włodzimierz Wysocki |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Statistics and Probability
Hilbert cube Statistics::Theory Pure mathematics N dimensional Laplace transform Kendall tau rank correlation coefficient Mathematical analysis Copula (linguistics) Nonparametric statistics Univariate Statistics::Other Statistics Monotone polygon Statistics::Methodology Statistics Probability and Uncertainty Mathematics |
| Zdroj: | Journal of Nonparametric Statistics. 27:442-459 |
| ISSN: | 1029-0311 1048-5252 |
| DOI: | 10.1080/10485252.2015.1070849 |
| Popis: | We derive formulas for the dependence measures and for Archimedean n-copulas. These measures are n-dimensional analogues of the popular nonparametric dependence measures: Kendall's tau and Spearman's rho. For we obtain two formulas, both involving integrals of univariate functions. The formulas for involve integrals of n-variate functions. We also obtain formulas for the three measures for copulas whose additive generators have completely monotone inverses. These formulas feature integrals of 2-variate functions (we use the Laplace transform). We study the asymptotic properties of the sequences and , for a sequence of Archimedean copulas with a common additive generator. We also investigate the limit of this sequence, which is an infinite-dimensional copula on the Hilbert cube. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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