Geometric interpretation of the residual dependence coefficient. (English) Zbl 1360.60100
Summary: The residual dependence coefficient was originally introduced by A. W. Ledford and J. A. Tawn [Biometrika 83, No. 1, 169–187 (1996; Zbl 0865.62040)] as a measure of residual dependence between extreme values in the presence of asymptotic independence. We present a geometric interpretation of this coefficient with the additional assumptions that the random samples from a given distribution can be scaled to converge onto a limit set and that the marginal distributions have Weibull-type tails. This result leads to simple and intuitive computations of the residual dependence coefficient for a variety of distributions.
MSC:
| 60G70 | Extreme value theory; extremal stochastic processes |
| 62G20 | Asymptotic properties of nonparametric inference |
| 62G32 | Statistics of extreme values; tail inference |
Keywords:
asymptotic independence; residual dependence coefficient; sample clouds; limit set; multivariate density; geometric approachCitations:
Zbl 0865.62040Software:
QRMReferences:
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