Publicação
Estimation Pareto tail index based on sample means
| 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. |
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| 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 |
| 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. |
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