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

作者：S. Benchaira, Saida Mancer, A. Necir · 发表于：International Journal of Applied Mathematics and Simulation · 年份：2024 · DOI：10.69717/ijams.v1.i2.99

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. MSC: Primary 62G32, 62G30, Secondary 60G70, 60F17 REFERENCES [1] Alexander, K. S. (1986). Sample moduli for set-indexed Gaussian processes. The Annals of Probability, 14(2), 598-611. Search in Google Scholar.  https://doi.org/10.1214/aop/1176992533 [2] Benchaira, S., Meraghni, D., & Necir, A. (2015). On the asymptotic normality of the extreme value index for right-truncated data. Statistics & Probability Letters, 107, 378-384. Search in Google Scholar. https://doi.org/10.1016/j.spl.2015.08.031 [3] Benchaira, S., Meraghni, D., & Necir, A. (2016). Tail product-limit process for truncated data with application to extreme value index estimation. Extremes, 19(2), 219-251. Search in Google Scholar.   https://doi.org/10.1007/s10687-016-0241-9 [4] Benchaira, S., Meraghni, D., & Necir, A. (2016). Kernel estimation of the tail index of a right-truncated Pareto-type distribution. Statistics &...