Nonparametric Robust Estimator for Slope Parameter in Linear Structural Relationship Model

Abstract

In this study, the slope parameter of linear structural relationship model is determined by using the proposed robust nonparametric method based on trimmed mean. This method is an upgrade to the nonparametric method that was introduced by Al-Nasser et al. (2005) by employing trimmed mean for all likely paired slopes rather than median slopes. Simulation study and real data were used to compare the proposed method’s performance versus the traditional maximum likelihood method. In the simulation study, based on both methods’ mean square error, it was inferred that the MLE method break down due to the presence of outliers even though its elaborate was not affected when there was no outlier in the data set. Based on the real life examples, it can be concluded that the performance of our proposed method was better in determining the slope parameter and thus provides a good alternative to MLE method when outliers are present.