2021/11/04 by Abdelaati Daouia, Daouia, Abdelaati, Simone A. Padoan +3
Economics, Econometrics and Finance · Environmental Science · Mathematics · Social Sciences · #62F10 #62F12 #62G30 #62G32 #FOS: Computer and information sciences #FOS: Mathematics #Financial Risk and Volatility Modeling #Hydrology and Drought Analysis #Insurance, Mortality, Demography, Risk Management #Methodology (stat.ME) #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2111.03173
openalex publication_date 2021/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper investigates pooling strategies for tail index and extreme\nquantile estimation from heavy-tailed data. To fully exploit the information\ncontained in several samples, we present general weighted pooled Hill\nestimators of the tail index and weighted pooled Weissman estimators of extreme\nquantiles calculated through a nonstandard geometric averaging scheme. We\ndevelop their large-sample asymptotic theory across a fixed number of samples,\ncovering the general framework of heterogeneous sample sizes with different and\nasymptotically dependent distributions. Our results include optimal choices of\npooling weights based on asymptotic variance and MSE minimization. In the\nimportant application of distributed inference, we prove that the\nvariance-optimal distributed estimators are asymptotically equivalent to the\nbenchmark Hill and Weissman estimators based on the unfeasible combination of\nsubsamples, while the AMSE-optimal distributed estimators enjoy a smaller AMSE\nthan the benchmarks in the case of large bias. We consider additional scenarios\nwhere the number of subsamples grows with the total sample size and effective\nsubsample sizes can be low. We extend our methodology to handle serial\ndependence and the presence of covariates. Simulations confirm that our pooled\nestimators perform virtually as well as the benchmark estimators. Two\napplications to real weather and insurance data are showcased.\n