Consistency of full-sample bootstrap for estimating high-quantile, tail probability, and tail index

Svetlana Litvinova () and Mervyn Silvapulle ()

No 15/20, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: We show that the full-sample bootstrap is asymptotically valid for constructing confidence intervals for high-quantiles, tail probabilities, and other tail parameters of a univariate distribution. This resolves the doubts that have been raised about the validity of such bootstrap methods. In our extensive simulation study, the overall performance of the bootstrap method was better than that of the standard asymptotic method, indicating that the bootstrap method is at least as good, if not better than, the asymptotic method for inference. This paper also lays the foundation for developing bootstrap methods for inference about tail events in multivariate statistics; this is particularly important because some of the non-bootstrap methods are complex.

Keywords: full-sample bootstrap; intermediate order statistic; extreme value index; Hill estimator; tail probability; tail quantile (search for similar items in EconPapers)
JEL-codes: C13 C15 C18 (search for similar items in EconPapers)
Pages: 41
Date: 2020
New Economics Papers: this item is included in nep-ecm, nep-gen, nep-ore and nep-rmg
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