Weighting GM6 Method to Estimate High Robustness Coefficients for a Multiple Regression Model

Abstract

The multiple linear regression model is one of the most widely used statistical methods in many scientific fields. The model parameters are estimated using the ordinary least squares method, which gives the best unbiased linear estimate when its assumptions are met. One of these assumptions is that the distribution of the random error term is normal with a mean of zero and a constant variance. The presence of outliers leads to a violation of this assumption, and therefore the least squares method cannot be applied. Robust methods have emerged as a suitable alternative when outliers appear, such as the M method, LMS, LTS, and the S estimator. However, the appearance of leverage points as another type of outlier in the space of explanatory variables has led to inaccuracy in the estimates of these methods. Very distinctive methods have been proposed in the statistical literature, such as the MM estimator method and the GM6 method, but the emergence of the problem of high leverage points, the reason for whose existence is attributed to the emergence of the phenomena of (Masking and Swamping). These two phenomena indicate inaccuracy in diagnosing leverage points, which causes either a loss of information or failure to completely treat bad leverage points. The proposal of this research seeks to improve the performance of the GM6 method, even in the presence of these two phenomena, by employing a high-precision diagnostic algorithm called IDRGP (RMVN) in order to obtain high-precision weights to reduce the impact of leverage points in the GM6 method. We have put the accurate diagnosis and GM6 method into a single algorithmic framework that we called GM6.IDRGP(RMVN), which showed outstanding performance compared to previous methods through the results of simulation studies and real data.