A Robust Method to Estimate the Slope Parameter in Linear Functional Relationship Model

摘要

This paper proposed a robust nonparametric method to estimate the slope parameter of a linear functional relationship model in which both parameters are subject to error. The method is an improvement to the nonparametric method as proposed by Al-Nasser [1]. The performance of the proposed method is compared to the traditional maximum likelihood method using Monte Carlo simulation study. The mean square error of both these two methods gave somewhat similar results when no outlier exists, however as the percentage of outlier increases, the maximum likelihood method seems quite unreliable as its mean square error breaks down easily and became huge. Based on these findings, we can conclude that as the percentage of outlier increases, our proposed method gave significantly smaller mean square error than the nonparametric method [1]. Application of the proposed method is illustrated using two published datasets.