On optimising the estimation of high quantiles of a probability distribution

A. Ferreira, L. Haan, de, L. Peng

Research output: Contribution to journalArticleAcademicpeer-review

74 Citations (Scopus)
7 Downloads (Pure)

Abstract

One of the major aims of one-dimensional extreme-value theory is to estimate quantiles outside the sample or at the boundary of the sample. The underlying idea of any method to do this is to estimate a quantile well inside the sample but near the boundary and then to shift it somehow to the right place. The choice of this "anchor quantile" plays a major role in the accuracy of the method. We present a bootstrap method to achieve the optimal choice of sample fraction in the estimation of either high quantile or endpoint estimation which extends earlier results by Hall and Weissman (1997) in the case of high quantile estimation. We give detailed results for the estimators used by Dekkers et al. (1989). An alternative way of attacking problems like this one is given in a paper by Drees and Kaufmann (1998).
Original languageEnglish
Pages (from-to)401-434
JournalStatistics
Volume37
Issue number5
DOIs
Publication statusPublished - 2003

Fingerprint

Dive into the research topics of 'On optimising the estimation of high quantiles of a probability distribution'. Together they form a unique fingerprint.

Cite this