A0788
Title: Bootstrap for the vector tail empirical process
Authors: Jun-ichiro Fukuchi - Gakushuin University (Japan) [presenting]
Abstract: A prior study derived the limiting process of the bootstrapped tail empirical process and its integral functional. Their results are extended to the vector tail empirical process (the vector TEP) based on the sample of a multivariate population. First, it is proved that the vector TEP converges weakly to a centered Gaussian process if the two-dimensional marginal distribution function admits an upper tail copula. Second, the limit of the bootstrapped vector TEP is derived. As a result, Efron's bootstrap is shown to be consistent for integral functionals under the no-bias assumption. As an application, a method of selecting the components is considered, whose high quantiles are the larger than a given value, which rely on the consistency of the bootstrap.
