On the Robust Estimations of Location and Scale Parameters for Least Informative Distributions

Abstract

M-estimation as generalization of maximum likelihood estimation (MLE) method is well-known approach to get the robust estimations of location and scale parameters in objective function ? especially. Maximum log_q likelihood estimation (MLqE) method uses different objective function called as ?_(log_q ). These objective functions are called as M-functions which can be used to fit data set. The least informative distribution (LID) is convex combination of two probability density functions f_0 and f_1. In this study, the location and scale parameters in any objective functions ?_log, ?_(log_q ) and ?_(log_q ) (f_0,f_1 ) which are from MLE, MLqE and LIDs in MLqE are estimated robustly and simultaneously. The probability density functions which are f_0 and f_1 underlying and contamination distributions respectively are chosen from exponential power (EP) distributions, since EP has shape parameter ? to fit data efficiently. In order to estimate the location ? and scale ? parameters, Huber M-estimation, MLE of generalized t (Gt) distribution are also used. Finally, we test the fitting performance of objective functions by using a real data set. The numerical results showed that ?_(log_q ) (f_0,f_1 ) is more resistance values of estimates for ? and ? when compared with other ? functions.