论文信息 - Approximation rates for multivariate exceedances

Approximation rates for multivariate exceedances

Abstract This article deals with the Poisson approximation of processes of pathwise or componentwise defined exceedances; the approximations are carried out in terms of the variational distance. Bounds on the accuracy of these approximations are given by means of survivor functions. Moreover, the concept of a δ-neighborhood of a generalized Pareto d.f. will be extended from the univariate setting to the bivariate one. Finally, approximate distributions of bivariate extreme and intermediate order statistics are deduced from the point process result.

Rolf-Dieter Reiss | Edgar Kaufmann

[1] Rates of convergence in multivariate extreme value theory , 1991 .

[2] Poisson approximation of empirical processes , 1992 .

[3] R. Reiss. Approximate Distributions of Order Statistics: With Applications to Nonparametric Statistics , 1989 .

[4] Lionel Weiss,et al. Asymptotic inference about a density function at an end of its range , 1971 .

[5] J. D. T. Oliveira,et al. The Asymptotic Theory of Extreme Order Statistics , 1979 .

[6] S. Resnick. Extreme Values, Regular Variation, and Point Processes , 1987 .

[7] J. Pickands. Statistical Inference Using Extreme Order Statistics , 1975 .

[8] Rolf-Dieter Reiss,et al. Strong convergence of multivariate point processes of exceedances , 1993 .

[9] L. Haan,et al. Residual Life Time at Great Age , 1974 .

[10] Michael Falk,et al. Von Mises Conditions Revisited , 1993 .

[11] Rolf-Dieter Reiss,et al. A Course on Point Processes , 1992 .

[12] Reiss R.-D.. ASYMPTOTIC INDEPENDENCE OF MARGINAL POINT PROCESSES OF EXCEEDANCES , 1990 .