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

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Gomes M., Henriques-Rodrigues L.

Discussiones Mathematicae Probability and Statistics

2010

tom 30

nr 1

35-51

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.

An asymptotically unbiased moment estimator of a negative extreme value index

100%

Caeiro F., Gomes M.

Discussiones Mathematicae Probability and Statistics

2010

tom 30

nr 1

5-19

In this paper we consider a new class of consistent semi-parametric estimators of a negative extreme value index, based on the set of the k largest observations. This class of estimators depends on a control or tuning parameter, which enables us to have access to an estimator with a null second-order component of asymptotic bias, and with a rather interesting mean squared error, as a function of k. We study the consistency and asymptotic normality of the proposed estimators. Their finite sample behaviour is obtained through Monte Carlo simulation.

Ograniczanie wyników

2 Discussiones Mathematicae Probability and Statistics

2 Gomes M.

1 Caeiro F.

1 Henriques-Rodrigues L.

2 2010

Wyniki wyszukiwania

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

An asymptotically unbiased moment estimator of a negative extreme value index