Modified ratio estimators using robust regression methods

What is it about?

Whenthere is an outlier in the data set, the efficiency of traditionalmethods decreases. In order to solve this problem, Kadilar et al. (2007) adapted Huber-M method which is only one of robust regression methods to ratio-type estimators and decreased the effect of outlier problem. In this study, new ratio-type estimators are proposed by considering Tukey-M, Hampel M, Huber MM, LTS, LMS and LAD robust methods based on the Kadilar et al. (2007). Theoretically,we obtain the mean square error (MSE) for these estimators.We comparedwithMSE values of proposed estimators andMSE values of estimators based on Huber-M and OLSmethods. As a result of these comparisons, we observed that our proposed estimators give more efficient results than both Huber M approach which was proposed by Kadilar et al. (2007) and OLS approach. Also, under all conditions, all of the other proposed estimators except Lad method are more efficient than robust estimators proposed by Kadilar et al. (2007). And, these theoretical results are supported with the aid of a numerical example and simulation by basing on data that includes an outlier.

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Why is it important?

The main aim of this study is to reduce the effect of the outlier problem by using some of the robust regression methods in addition to Huber-Mestimates used by Kadılar, Candan, and Çıngı (2007), and to improve upon the approach proposed by Kadılar, Candan, and Çıngı (2007).