Comparison of some robust estimators for multiple linear regression model parameter estimation with the presence of high leverage points by simulation

Abstract

The multiple linear regression model is one of the linear models widely used to analyze many research data in the economic, medical and social fields, and the research aims to obtain high-efficiency capabilities that the presence of outliers affects this efficiency and the presence of outliers observations (high leverage points must be detected), In the illustrative variables and treating them by estimating the parameters using some of the invulnerable estimation methods illustrated through the research, the M estimator, the MM estimator, the S estimator and the GM2 estimator. In order to know the best of the estimators, a simulation method was used between estimation methods with different sample sizes  and assuming different Contamination ratios  and based on the comparison criterion average squares of error (MSE) For the model to reach the best method, the results showed that the (MM) estimator achieved high efficiency in estimating the parameters compared with the rest of the estimators.

As for the application side of this study, real data taken from the Central Bureau of Statistics was employed regarding the results of the survey questionnaire for the Food Security and Vulnerability Assessment of Households in Iraq for the year 2016, by describing the data represented by the estimated average monthly expenditure of the head of the household on non-food goods and services. We notice the presence of four observations with high leverage points in the data, and these observations are (23,46,53,94) as they were revealed by the main country components of the Hat Matrix, as well as from the results of the application, we note the significance of the variable of the head of the household's total expenditure on education and the variable of total housing spending Electricity and other fuels.