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

Authors : Mehmet Niyazi ÇANKAYA

Pages : 71-78

View : 16 | Download : 11

Publication Date : 2020-09-24

Article Type : Research Paper

Abstract :M-estimation as generalization of maximum likelihood estimation insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(MLqE); method uses different objective function called as ρ_insert ignore into journalissuearticles values(log_q );. These objective functions are called as M-functions which can be used to fit data set. The least informative distribution insert ignore into journalissuearticles values(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_insert ignore into journalissuearticles values(log_q ); and ψ_insert ignore into journalissuearticles values(log_q ); insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(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_insert ignore into journalissuearticles values(log_q ); insert ignore into journalissuearticles values(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