The Comparison of the Estimators for the Parameters of the General Linear Regression Model via Simulation and Two Real Life Data Examples
Makaleler > Tam Makale · 2019
Yazarlar: Nalan MUTLU, Hakan Savaş SAZAK
Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Diğer Kurumların Hakemli Dergileri, Uluslararası, Index Copernicus, 2019, cilt 23, ss 119-130
DOI: 10.19113/sdufenbed.538869
Özet
In this study we compared the efficiency and robustness of several estimators, namely, the least squares (LS) estimators, the Huber and Tukey M-estimators, the S-estimators and the MM-estimators for the parameters of the general linear regression (GLR) model via simulation. First, the programs for each method were written by using Matlab. Then, an extensive simulation study was conducted under several models. The results are consistent with the literature but some important points were also found to be remarked. As the literature suggests, in general, the MM-estimators are the most efficient estimators, and among the robust estimators discussed here, the S-estimators are the least efficient ones. Naturally, the LS estimators are badly affected by the deviations from the assumed model because of their sensitive nature. Moreover, it was found that while the LS estimator of the variance of the error term is unbiased, the robust estimators discussed here are generally biased. Additionally, the MM-estimator of the variance of the error term is less biased than the other robust estimators and its bias gets smaller faster as the sample size increases compared to the others. At the end of the study, to be more illustrative, two real life data examples were given with the related comments.