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Abstract <p>The Box-Cox transformation is used to enhance data suitability for statistical analysis. When applied to extreme value statistics, it increases the convergence rate of several estimators for the tail index and mitigates their bias in the context of independent and identically distributed (i.i.d.) random variables. This paper focuses on investigating an estimator designed for bias reduction of the extreme value index estimators within the context of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12004_2025_5063_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta\)</EquationSource> <!--MMStat2460007Diouf-m1--> </InlineEquation>-mixing serial dependence, employing the Box-Cox transformation. Under specific regular conditions, we establish the asymptotic normality of the suggested estimator and derive an estimator for high quantiles that is asymptotically unbiased. Through a simulation study, we emphasize the performance of our proposals, comparing them with alternative estimators recently introduced in the literature. Also, we apply our methodology on real data of nitrogen dioxide (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12004_2025_5063_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(NO_{2}\)</EquationSource> <!--MMStat2460007Diouf-m2--> </InlineEquation>) concentration.</p>

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Box-Cox Transformation on the Estimation of Extreme Value Index (EVI) and High Quantiles for Heavy-Tailed Distributions under Dependence Serials

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Mame Birame Diouf,
  • El Hadji Deme,
  • Sidi Ali Abdi,
  • Yousri Slaoui,
  • Solym M. Manou-Abi

摘要

Abstract

The Box-Cox transformation is used to enhance data suitability for statistical analysis. When applied to extreme value statistics, it increases the convergence rate of several estimators for the tail index and mitigates their bias in the context of independent and identically distributed (i.i.d.) random variables. This paper focuses on investigating an estimator designed for bias reduction of the extreme value index estimators within the context of \(\beta\) -mixing serial dependence, employing the Box-Cox transformation. Under specific regular conditions, we establish the asymptotic normality of the suggested estimator and derive an estimator for high quantiles that is asymptotically unbiased. Through a simulation study, we emphasize the performance of our proposals, comparing them with alternative estimators recently introduced in the literature. Also, we apply our methodology on real data of nitrogen dioxide ( \(NO_{2}\) ) concentration.