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

2022/07/16 by Yongcheng Qi, Qi, Yongcheng, Mengzi Xie +3
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2207.07988

openalex publication_date 2022/07/16 · openalex created_date 2022/07/21 · openalex updated_date 2026/08/01

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.

Related

• Profile Likelihood Intervals for Quantiles in Extreme Value Distributions
• A Bias-reduced Estimator for the Mean of a Heavy-tailed Distribution\n with an Infinite Second Moment
• Empirical Likelihood based Confidence Regions for first order parameters of a heavy tailed distribution
• Optimal pooling and distributed inference for the tail index and extreme\n quantiles
• Confidence Intervals for Quantiles from Histograms and Other Grouped Data