New Robust Weighted Grouping Method for Multiple Models

Abstract

In this paper, three new estimation methods are proposed to fit a multiple structural measurement error model with two independent variables when all variables are subject to errors. The first two procedures are modifications of the Theil and Siegel estimators, where they involved the proposed Weighted Latent Variables method, while the third procedure is Iterative Weighted Grouping, an extension of Wald estimation that involved the Weighted Grouping method. A Monte Carlo experiment is performed to investigate the performance of the new estimators compared with the classical estimation methods; the Maximum Likelihood Estimator and Method of Moment, in terms of root mean square error and its bias. The outcomes of the simulation demonstrated that the suggested estimators are more effective than conventional estimators. In addition, real data analysis is discussed to examine the relationship between national gross domestic product, unemployment rate, and human development index, after applying the proposed estimation methods.

Keywords: Model of Measurement Error; Robust Estimators; Iterative Estimator; Human Development Index; Unemployment Rate;
National Gross Domestic Product; Monte Carlo Simulation.

2010 Mathematics Subject Classification. 26A25; 26A35