Robust Estimation of the Pareto Index: A Monte Carlo Analysis

Abstract

The Pareto distribution is often used in many areas of economics to model the right tail of heavy-tailed distributions. However, the standard method of estimating the shape parameter (the Pareto index) of this distribution – the maximum likelihood estimator (MLE) – is non-robust, in the sense that it is very sensitive to extreme observations, data contamination or model deviation. In recent years, a number of robust estimators for the Pareto index have been proposed, which correct the deficiency of the MLE. However, little is known about the performance of these estimators in small-sample setting, which often occurs in practice. This paper investigates the small-sample properties of the most popular robust estimators for the Pareto index, including the optimal B-robust estimator (OBRE) (Victoria-Feser and Ronchetti, 1994, The Canadian Journal of Statistics 22:247-258), the weighted maximum likelihood estimator (WMLE) (Dupuis and Victoria-Feser, 2006, Canadian Journal of Statistics 34:639-658), the generalized median estimator (GME) (Brazauskas and Serfling, 2001a, Extremes 3, 231-249), the partial density component estimator (PDCE) (Vandewalle et al., 2007, Computational Statistics & Data Analysis 51:6252-6268), and the probability integral transform statistic estimator (PITSE) (Finkelstein et al., 2006, North American Actuarial Journal 10, 1-10). Monte Carlo simulations show that the PITSE offers the desired compromise between ease of use and power to protect against outliers in the small-sample setting.