Adaptive Robust Estimation Based on a Family of Generalized Exponential Power Distributions

Abstract

This paper suggests using the family of exponential power (EP) distributions to model data which are believed (a priori) to be essentially symmetric but where the usual assumptions of s-normality is unwarranted. Four estimation procedures are proposed for the parameters of the distribution. Two procedures are based on variations of the method of maximum likelihood (ML) while the other two use the method of moments to estimate the shape parameter but employ ML to estimate the location and scale parameters of the model. A Monte Carlo analysis compares the mean square errors of the estimators of the location and scale parameters of the model. Sample sizes 4(4)28 were drawn 2000 times from five symmetric probability distributions. A minimax criterion was used to evaluate each of the estimators. Comparison with adaptive and nonadaptive estimates of location and scale parameters show that the new procedure provides: 1) good estimates of scale and location parameters, and 2) a complete probability model for the data.