A Bias-reduced Estimator for the Mean of a Heavy-tailed Distribution with an Infinite Second Moment

2012/01/07 by Brahim Brahimi, Djamel Meraghni, Brahimi, Brahim +5
Mathematics · #62E20 #62G32 #65C05 #Advanced Statistical Methods and Models #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST) #math.ST #msc:62E20 #msc:62G32 #msc:65C05 #stat.CO #stat.ME #stat.TH

paper · pdf · doi:10.48550/arxiv.1201.1578

Submitted

openalex publication_date 2012/01/07 · arxiv created 2012/01/10 · arxiv updated 2014/05/09 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We use bias-reduced estimators of high quantiles, of heavy-tailed distributions, to introduce a new estimator of the mean in the case of infinite second moment. The asymptotic normality of the proposed estimator is established and checked, in a simulation study, by four of the most popular goodness-of-fit tests for different sample sizes. Moreover, we compare, in terms of bias and mean squared error, our estimator with Peng's estimator (Peng, 2001) and we evaluate the accuracy of some resulting confidence intervals.

Related

• Estimating the mean of a heavy-tailed distribution under random censoring
• A new method for estimating the tail index using truncated sample sequence
• A Log Probability Weighted Moment Estimator of Extreme Quantiles
• Inference of high quantiles of a heavy-tailed distribution from block data
• High confidence estimates of the mean of heavy-tailed real random variables