Estimation of regression model parameters by the trimmed maximum likelihood method
The new method of estimating the parameters of regression equations named a trimmed maximum likelihood method is proposed in this paper. This method is based on combining the maximum likelihood method and the trimmed least squares method. The problem of constructing a linear model of regression analysis is formulated. To do this an algorithm of the trimmed maximum likelihood method is described in detail and the main principles which form the basis of the algorithm are demonstrated on a simple example. The task of robustness analysis of regression model parameter estimates is substantiated. The analysis of the proposed algorithm efficiency is made using computing experiment methods. Simulation of random errors in computing experiments was conducted by Monte-Carlo methods. The distribution of random errors was modeled as a mixture of two distributions. Normal distribution was considered as the base distribution of random errors. The estimation of regression model parameters was conducted using least squares, trimmed least squares and trimmed maximum likelihood methods. A relative error of regression model parameter estimation was used as a precision measure. Such types of contamination, as unbiased with a zero mean, symmetric and asymmetric contaminations were considered. The ratio of outliers varied from 2.5 to 20 percent. A series of 100 experiments whose results were averaged was carried out for each type of original data contaminations. The results of computational experiments have shown that the trimmed maximum likelihood method has good robustness to various types of contaminations of original data. In most cases, it is almost as good as the trimmed least squares method, and in some cases significantly exceeds it in accuracy.