ACTA issues

Regression estimators for the tail index

Amenah AL-Najafi, László L. Stachó, László Viharos

Acta Sci. Math. (Szeged) 87:3-4(2021), 649-678

Abstract. We propose a class of weighted least squares estimators for the tail index of a distribution function with a regularly varying tail. Our approach is based on the method developed by Holan and McElroy (2010) for the Parzen tail index. We prove asymptotic normality and consistency for the estimators under suitable assumptions. These and earlier estimators are compared in various models through a simulation study using the mean squared error as criterion. The results show that the weighted least squares estimator has good performance.

DOI: 10.14232/actasm-020-361-6

AMS Subject Classification (1991): 60F05, 62G32

Keyword(s): tail index, Pareto model, weighted least squares estimators, quantile process

received 11.6.2020, revised 31.8.2021, accepted 2.9.2021. (Registered under 611/2020.)