A comparative study between the two methods GM6.IDRGP(RMVN) and the GM6 method for analyzing the multiple linear regression model in the presence of outliers using the simulation method.

Abstract

Multiple linear regression is one of the most widely used statistical analysis methods in many scientific fields. Its parameters are estimated based on the ordinary least squares method. Which gives the best unbiased linear estimate if its assumptions are met. The most important of these assumptions is that it has a normal distribution of error with a mean of zero and a constant variance. If the data does not meet certain assumptions, the sample estimates and results may be misleading. The linear regression model is sensitive to the appearance of outliers and leverage points. Therefore, statistical techniques have been developed capable of dealing with or detecting outliers. This led to the emergence of many alternative methods to the OLS method, such as M-Huber, s, LTS, and MM, which have high efficiency and breakdown points, but are affected by HLPs, which result in the problem of Masking and Swamping. The GM6 method is one of the methods that was developed in order to treat such problems through the use of a weight function, but the weight function depends on the individual diagnosis, which gives inaccurate results. In order to overcome this problem, comprehensive diagnostic methods have been proposed, such as the DRGP and IDRGP.RMVN methods. Therefore, in this study, we proposed to employ the IDRGP.RMVN method in the GM6 method algorithm. And comparing it with some hippocampal regression methods through a simulation study in determining the best methods.