Parameter estimation in replicated linear functional relationship model in the presence of outliers

Abstract

The relationship between two linear variables where both variables are observed with errors can be modeled using a linear functional relationship model. However, when there is no knowledge about the ratio of error variance, we proposed that one can use the replicated linear functional relationship model. The aim of this study is to compare the parameter estimates between unreplicated and replicated linear functional relationship model. The study also extends to examine the behavior of the estimators of the replicated linear functional relationship model in the presence of outliers. A simulation study is performed to investigate the performance of the model. In the absence of outlier, it is found that the value of the parameter estimates is almost similar for both models. Whereas in the presence of outliers, the parameter estimates of the replicated linear functional relationship model have a smaller mean square error as the number of observations increased. This suggests the superiority of the replicated model.