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Estimation Pareto tail index based on sample means

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Detalhes bibliográficos
Resumo:We propose an estimator of the Pareto tail index m of a distribution, that competes well with the Hill, Pickands and moment estimators. Unlike the above estimators, that are based only on the extreme observations, the proposed estimator uses all observations; its idea rests in the tail behavior of the sample mean X¯n, having a simple structure under heavy-tailed F. The observations, partitioned into N independent samples of sizes n, lead to N sample means whose empirical distribution function is the main estimation tool. The estimator is strongly consistent and asymptotically normal as N → ∞, while n remains fixed. Its behavior is illustrated in a simulation study.
Autores principais:Fialová, Alena
Outros Autores:Jurečková, Jana; Picek, Jan
Assunto:domain of attraction Pareto index strong embedding of empirical process tail behavior
Ano:2004
País:Portugal
Tipo de documento:artigo
Tipo de acesso:unknown
Instituição associada:Instituto Nacional de Estatística
Idioma:inglês
Origem:REVSTAT-Statistical Journal
Descrição
Resumo:We propose an estimator of the Pareto tail index m of a distribution, that competes well with the Hill, Pickands and moment estimators. Unlike the above estimators, that are based only on the extreme observations, the proposed estimator uses all observations; its idea rests in the tail behavior of the sample mean X¯n, having a simple structure under heavy-tailed F. The observations, partitioned into N independent samples of sizes n, lead to N sample means whose empirical distribution function is the main estimation tool. The estimator is strongly consistent and asymptotically normal as N → ∞, while n remains fixed. Its behavior is illustrated in a simulation study.