Bootstrapping endpoint

Abstract

It is known that bootstrapping maximum for estimating the endpoint of a distribution function is inconsistent and subsample bootstrap method is needed. Under an extreme value condition, some other estimators for the endpoint have been studied in the literature, which are preferrable to the maximum in regular cases. In this paper, we show that the full sample bootstrap method is consistent for the endpoint estimator proposed by Hall (1982).

Estimation of the finite right endpoint in the Gumbel domain

“…In fact, the problem of estimating x F still gathers a great in-terest nowadays. Recently, Girard et al (2012) devised an endpoint estimator from the high-order moments pertaining to a distribution attached with γ < 0; Li and Peng (2012) proposed a bootstrap estimator for the endpoint evolving from the one by Hall (1982) in case γ ∈ (−1/2, 0). The present paper deliberately addresses the class of distribution functions belonging to the Gumbel domain of attraction, for which no specific inference has yet been provided in the context of estimation of the right endpoint x F < ∞.…”

Estimation of the finite right endpoint in the Gumbel domain

“…In fact, the problem of estimating x F still gathers a great interest nowadays. Recently, Girard et al (2012) devised an endpoint estimator from the high-order moments pertaining to a distribution attached with γ < 0; Li and Peng (2012) proposed a bootstrap estimator for the endpoint evolving from the one by Hall (1982) in case γ ∈ (−1/2, 0). The present paper deliberately addresses the class of distribution functions belonging to the Gumbel domain of attraction, for which no specific inference has yet been provided in the context of estimation of the right endpoint x F < ∞.…”