A supermartingale argument for characterizing the Functional Hill\n process weak law for small parameters

2013/06/23 by Gane Samb Lô, Adja Mbarka Fall, Lo, Gane Samb +5
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60F05. Secondary 60B10 #60F17 #62F12 #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Methodology (stat.ME) #Primary 62E20 #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1306.5462

openalex publication_date 2013/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper deals with the asymptotic laws of functional of standard random\nvariables. These classes of statistics are closely related to estimators of the\nextreme value index when the underlying distribution function is in the Weibull\ndomain of attraction. We use techniques based on martingales theory to describe\nthe non Gaussian asymptotic distribution of the aforementioned statistics. We\nprovide results of a simulation study as well as statistical tests that may be\nof interest with the proposed results.\n

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