A Log-Probability-Weighted-Moments type estimator for the extreme value index in a truncation scheme

Résumé

The limit theorems of asymptotic behavior of tail index estimators for right truncation Pareto-like data requires some regularity assumptions either on tail indices (γ1 < γ2) or on the dependence structure condition between the truncation variable and the interest one. In this paper, we introduce a new estimator for the tail index based on the Log-Probability-Weighted-Moments method and, getting rid of aforementioned assumptions, we establish its consistency and asymptotic normality. We show, by simulation, that the newly proposed estimator behaves well both in terms of bias and mean squared error.

Keywords: Empirical process, Extreme value index, Product-limit estimator, Truncated data.

MSC: Primary 62G32, 62G30, Secondary 60G70, 60F17

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Communicated Editor: Cherfaoui Mouloud

Manuscript received Jan 23, 2024; revised May 13, 2024; accepted May 18, 2024; published Dec 07, 2024.