Optimal weighted pooling for inference about the tail index and extreme quantiles

Abdelaati Daouia (), Simone A. Padoan and Gilles Stupfler

No 22-1322, TSE Working Papers from Toulouse School of Economics (TSE)

Abstract: This paper investigates pooling strategies for tail index and extreme quantile estimation from heavy-tailed data. To fully exploit the information contained in several samples, we present general weighted pooled Hill estimators of the tail index and weighted pooled Weissman estimators of extreme quantiles calculated through a nonstandard geometric averaging scheme. We develop their large-sample asymptotic theory across a fixed number of samples, covering the general framework of heterogeneous sample sizes with di↵erent and asymptotically dependent distributions. Our results include optimal choices of pooling weights based on asymptotic variance and MSE minimization. In the important application of distributed inference, we prove that the variance-optimal distributed estimators are asymptotically equivalent to the benchmark Hill and Weissman estimators based on the unfeasible combination of subsamples, while the AMSE-optimal distributed estimators enjoy a smaller AMSE than the benchmarks in the case of large bias. We consider additional scenarios where the number of subsamples grows with the total sample size and e↵ective subsample sizes can be low. We extend our methodology to handle serial dependence and the presence of covariates. Simulations confirm the statistical inferential theory of our pooled estimators. Two applications to real weather and insurance data are showcased.

Keywords: Extreme values; Heavy tails; Distributed inference; Pooling; Testing (search for similar items in EconPapers)
Date: 2022-03-21, Revised 2023-06-07
New Economics Papers: this item is included in nep-ban, nep-ecm and nep-rmg
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