Comparative Analysis of Robust Estimates in Regression Models

This work is devoted to the comparative analysis of robust least median of squares (LMS) and least trimmed squares (LTS) estimation methods as well as a non-robust least squares estimation method (LS) in linear regression models in the case of different noise distributions in the model. The work presents the implementation of algorithms for robust estimates construction, simulation of regression models with different distributions of errors and regressors, numerical comparison of LMS, LTS and LS estimates as well as a comparison of asymptotic relative efficiency in the case of different distributions of errors. Furthermore, the linear regression model describing relationship between GDP and CO2 emissions is analyzed based on real data. As a result of the research, the efficiency of LS estimate and robust L-estimates was analyzed for models with different distributions of noise and regressors. The performance of methods was also evaluated in the real data model case. The robustness of L-estimates was shown in the case of "heavy-tailed" distributions, as well as in the factor space with leverage points case.