Confidence regions for high quantiles of a heavy tailed distribution

Details Confidence regions for high quantiles of a heavy tailed distribution Confidence regions for high quantiles of a heavy tailed distribution

2006-11-09

arxiv.org/abs/math/0611278v1

Annals of Statistics 2006, Vol. 34, No. 4, 1964-1986

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000000416 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053606000000416

Estimating high quantiles plays an important role in the context of risk management. This involves extrapolation of an unknown distribution function. In this paper we propose three methods, namely, the normal approximation method, the likelihood ratio method and the data tilting method, to construct confidence regions for high quantiles of a heavy tailed distribution. A simulation study prefers the data tilting method.

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