Generalized Sum Plots

Abstract

Sousa and Michailidis (2004) developed the sum plot based on the Hill (1975) estimator as a diagnostic tool for selecting the optimal k when the distribution is heavy tailed. We generalize their method to any consistent estimator with any tail type (heavy, normal and light tail). We illustrate the method associated to the generalized Hill estimator and the moment estimator. As an attempt to reduce the bias of the generalized Hill estimator, we propose new estimators based on the regression model which are based on the estimates of the generalized Hill estimator. Here weighted least squares and weighted trimmed least squares is proposed. The bias and the mean squared error (MSE) of the estimators is studied using a simulation study. A few practical examples are proposed.