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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 918-940 |
| Number of pages | 23 |
| Journal | Statistics |
| Volume | 57 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2023 |
Bibliographical note
Funding Information:The research of Yongcheng Qi was supported in part by the NSF of USA [grant number DMS-1916014]. The research of Jingping Yang was supported by the National Natural Science Foundation of China [grant number 12071016]. The authors would like to thank two anonymous referees for their constructive suggestions that led to improvement of the paper.
Publisher Copyright:
© 2023 Informa UK Limited, trading as Taylor & Francis Group.
Keywords
- Heavy tailed distribution
- confidence interval
- coverage probability
- empirical likelihood
- high quantile