On bootstrap sample size in extreme value theory

It has been known for a long time that for bootstrapping theprobability distribution of the maximum of a sample consistently,the bootstrap sample size needs to be of smaller order than theoriginal sample size. See Jun Shao and Dongsheng Tu (1995), Ex.3.9,p. 123. We show that the same is true if we use the bootstrapfor estimating an intermediate quantile.Bootstrap;Regular variation

Von mises-type conditions in second order regular variation

We give a thorough treatment concerning sufficient conditions involving derivatives for extended regular variation of second order. Most of the results are new. A summary of the analogous (known) results for first order extended regular variation is given first

Estimating Extreme Bivariate Quantile Regions

AMS 2000 subject classifications. Primary 62G32, 62G05; secondary 60G70, 60F05.

Weighted Approximations of Tail Copula Processes with Application to Testing the Multivariate Extreme Value Condition

Consider n i.i.d. random vectors on R2, with unknown, common distribution function F.Under a sharpening of the extreme value condition on F, we derive a weighted approximation of the corresponding tail copula process.Then we construct a test to check whether the extreme value condition holds by comparing two estimators of the limiting extreme value distribution, one obtained from the tail copula process and the other obtained by first estimating the spectral measure which is then used as a building block for the limiting extreme value distribution.We derive the limiting distribution of the test statistic from the aforementioned weighted approximation.This limiting distribution contains unknown functional parameters.Therefore we show that a version with estimated parameters converges weakly to the true limiting distribution.Based on this result, the finite sample properties of our testing procedure are investigated through a simulation study.A real data application is also presented.approximations;multivariate analysis