Inference of high quantiles of a heavy-tailed distribution from block data

TL;DR

This paper develops estimators for high quantiles of heavy-tailed distributions from block data, proving their asymptotic normality and comparing confidence interval methods through simulations.

Contribution

It introduces new estimators for high quantiles from limited block data and applies empirical likelihood techniques for confidence interval construction.

Findings

Estimators are asymptotically normal.

Adjusted empirical likelihood improves confidence interval coverage.

Simulation shows better performance of empirical likelihood methods.

Abstract

In this paper we consider the estimation problem for high quantiles of a heavy-tailed distribution from block data when only a few largest values are observed within blocks. We propose estimators for high quantiles and prove that these estimators are asymptotically normal. Furthermore, we employ empirical likelihood method and adjusted empirical likelihood method to constructing the confidence intervals of high quantiles. Through a simulation study we also compare the performance of the normal approximation method and the adjusted empirical likelihood methods in terms of the coverage probability and length of the confidence intervals.