Comparison at optimal levels of classical tail index estimators: a challenge for reduced-bias estimation?

• Autorzy: M. Ivette Gomes , Lígia Henriques-Rodrigues
• Języki publikacji: EN

Abstrakty

EN

In this article, we begin with an asymptotic comparison at optimal levels of the so-called "maximum likelihood" (ML) extreme value index estimator, based on the excesses over a high random threshold, denoted PORT-ML, with PORT standing for peaks over random thresholds, with a similar ML estimator, denoted PORT-MP, with MP standing for modified-Pareto. The PORT-MP estimator is based on the same excesses, but with a trial of accommodation of bias on the Generalized Pareto model underlying those excesses. We next compare the behaviour of these ML implicit estimators with the equivalent behaviour of a few explicit tail index estimators, the Hill, the moment, the generalized Hill and the mixed moment. As expected, none of the estimators can always dominate the alternatives, even when we include second-order MVRB tail index estimators, with MVRB standing for minimum-variance reduced-bias. However, the asymptotic performance of the MVRB estimators is quite interesting and provides a challenge for a further study of these MVRB estimators at optimal levels.

Słowa kluczowe

EN

statistics of extremes; semi-parametric estimation; bias estimation; heavy tails; optimal levels

Kategorie tematyczne

• 65C05: Monte Carlo methods
• 62G32: Statistics of extreme values; tail inference

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2010
• Tom: 30
• Numer: 1
• Strony: 35-51

Daty

wydano

2010

otrzymano

2010-01-15

Twórcy

autor

M. Ivette Gomes

• DEIO and CEAUL, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal

autor

Lígia Henriques-Rodrigues

• Instituto Politécnico de Tomar and CEAUL

Bibliografia

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Identyfikatory

DOI

10.7151/dmps.1120