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How to improve the fit of Archimedean copulas by means of transforms. (English) Zbl 1440.62188

Summary: The selection of copulas is an important aspect of dependence modeling issues. In many practical applications, only a limited number of copulas is tested and the copula with the best result for a goodness-of-fit test is chosen, which, however, does not always lead to the best possible fit. In this paper we develop a practical and logical method for improving the goodness-of-fit of a particular Archimedean copula by means of transforms. In order to do this, we introduce concordance invariant transforms which can also be tail dependence preserving, based on an analysis on the \(\lambda\)-function, \(\lambda=\frac{\varphi}{\varphi'}\), where \(\varphi\) is the Archimedean generator. The methodology is applied to the data set studied in [R. D. Cook and M. E. Johnsson, J. R. Stat. Soc., Ser. B 43, 210–218 (1981; Zbl 0471.62046)] and C. Genest and L.-P. Rivest [J. Am. Stat. Assoc. 88, No. 423, 1034–1043 (1993; Zbl 0785.62032)], where we improve the fit of the Frank copula and obtain statistically significant results.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
60H20 Stochastic integral equations
62H12 Estimation in multivariate analysis
62G32 Statistics of extreme values; tail inference
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References:

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