Comparison of some robust estimation methods with deep regression methods

Abstract

The goal of any analytical method to obtain estimates that are very close to their parameters is to represent the population from which the sample was drawn well. When the distribution of a phenomenon is a normal distribution, i.e. it is subject to the established assumptions, then the usual methods such as the least squares method and the maximum likelihood method are efficient methods for obtaining good estimates, but the drawback of the arithmetic mean is that it is greatly affected in the case of the presence of outliers among the data taken, and in such a case, it is necessary to rely on another mediation or to carry out a data refinement process by identifying the outlier observations and compensating for them with alternative values. The function of statistical depth methods in regression is one of the modern methods that can be used to develop robust methods, especially in cases where the values ​​of the outlier observations are not changed based on robust estimates of the location and dispersion matrix, in order to provide robust estimation functions in the estimation and deeper for the location of the data, which have the desired robustness properties such as bias, the influence function, and the high breaking point that works in single-problem data and is insensitive to the presence of outliers and gives us efficient estimates. In this research, we relied on the robust M method and the repeated weighted least squares method. IRLS)), for the purpose of comparing its efficiency with the regression depth methods, which are the least squares method for residuals (LTS) and the regression depth method for mediators (RDM) for the purpose of obtaining the best estimator for the regression model based on the statistical criterion of the mean square error (MSE).