Averages of Hill Estimators

• Autores: M. Ivette Gomes, M. Joao Martins, M. Manuela Neves
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 13, Nº. 1, 2004, págs. 113-128
• Idioma: inglés
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• Resumen

  • Averaging Hill's estimators leads to a reduction in the volatility of Hill's plot. We deal with a generalization of the procedure proposed by Resnick and Starica (1997), and propose alternatives, asymptotically equivalent at the respective optimal levels, but with more interesting sample paths. Asymptotic normality is derived for intermediate levels where the asymptotic bias may be non-null. A simulation study completes the asymptotic results and shows the advantages of the proposed estimators in the problem of choosing the number of the top order statistics to be used in the estimation of the tail index.