ALTERNATIVE ESTIMATOR IN THE ANALYSIS OF VARIANCE TECHNIQUE IN THE PRESENCE OF OUTLIERS

Abstract

The estimation of ANOVA model parameters in the presence of outliers is one of the most pervasive problems in data analysis, statistical applications and inferences. The regularity of heavy tailed error distributions due to the presence of outliers in both experimental and observational data is of keen interest to researchers due its negative impact on most useful classical techniques in the field of statistical inferences. Authors at various times have examined empirically the problems of outliers in data analysis and inference from different considerations and various estimators including the classes of M estimators with fixed cut off point have been suggested in literature to address the limitations of the classical methods. Consequently, this paper examines the efficiency of the proposed alternative estimator: Adaptive Robust M Estimator (ARME) with data dependent (flexible) cut off point. The efficiency
(robustness) of the proposed method and the other existing methods: Huber M Fixed Cut off (HMFC), Bisquare M Fixed Cut off (BMFC) and Least Square Estimator (LSE) was compared using Monte Carlos simulated data for One-Way ANOVA with varying percentages of outliers on the response variable crossed with different sample size. The performance of the estimators was assess using Root Mean Square Error (RMSE). The results of the study revealed that the performance of the proposed estimator (ARME) is substantially better when compare with the existing methods using RMSE as measure of efficiency and goodness of fit at different degree of outliers.