Pareto Tail Index Estimation Revisited

Robust estimation of the Pareto tail index: a Monte Carlo analysis

“…2 If the Pareto distribution is the true model for a given sample, then one can safely estimate the Pareto tail index using MLE, which has the optimal asymptotic variance. However, in the presence of data contamination or when the sample deviates from the Pareto model, the MLE is not robust and becomes severely biased (Victoria-Feser and Ronchetti 1994;Finkelstein et al 2006). To make matters worse, even small errors in estimation of the Pareto exponent can produce large errors in estimation of quantities based on estimates of the exponent such as extreme quantiles, upper-tail probabilities and mean excess functions (Brazauskas and Serfling 2000).…”

“…In our Monte Carlo simulations, we useα (2) GME with k = 2 and k = 5, which correspond, respectively, to the ARE = 78 % and ARE = 94 %. Finkelstein et al (2006) noticed that since the distribution function of the Pareto model (1) is continuous and strictly increasing, the random variables…”

“…For all estimators under discussion, except for the PDCE, the trade-off between robustness and efficiency is regulated by the estimator's asymptotic properties. A comparison of the OBRE, GME and PITSE in terms of the upper breakdown point (UBP) and gross error sensitivity (GES) is presented in Finkelstein et al (2006).…”

“…The existing literature that examines the small-sample performance of alternative robust estimators for the Pareto exponent is fairly small (see Brazauskas and Serfling 2001b;Huisman et al 2001;Wagner and Marsh 2004;Finkelstein et al 2006;Alfons et al 2010). In addition, none of the existing studies compares all of the most popular robust estimators for the Pareto tail index.…”

“…We investigate the properties of the estimators by Monte Carlo simulations under various data contaminations and model deviations, which produce outliers that can be found in real data sets. In particular, the paper compares the optimal bias-robust estimator (OBRE) (Hampel et al 1986;Victoria-Feser and Ronchetti 1994), the weighted maximum likelihood estimator (WMLE) (Dupuis and Morgenthaler 2002;Dupuis and Victoria-Feser 2006), the generalized median estimator (GME) Serfling 2000, 2001a), the partial density component estimator (PDCE) (Vandewalle et al 2007) and the probability integral transform statistic estimator (PITSE) (Finkelstein et al 2006). 4 The OBRE, WMLE and PDCE have been applied in robust modelling of income distribution Victoria-Feser 2007, 2008;Alfons et al 2013).…”