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 ρ especially. Maximum log_q likelihood estimation (MLqE) method uses different objective function called as ρ_(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 ρ_log, ρ_(log_q ) and ψ_(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 α to fit data efficiently. In order to estimate the location μ and scale σ 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 ψ_(log_q ) (f_0,f_1 ) is more resistance values of estimates for μ and σ when compared with other ρ functions.

Keywords

• : Least informative distributions
• maximum log_q likelihood estimation method
• robustness

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