Research of the two-criteria estimation method for linear regression models
Mikhail P. Bazilevskiy - Associate Professor, Candidate of Technical Sciences, Associate Professor of the Department of Mathematics. Irkutsk State Transport University
Abstract
The paper is devoted to the research of the two-criteria estimation method for linear regressions. The first criterion corresponds to the least absolute deviations, the second – to the non-strict ordinary least squares. The implementation of the method requires solving a two-criteria linear programming problem, the solution of which involves the formation of a Pareto set. The main goal of the article was to research how the normalization of the initial variables affects the formation of the Pareto set. For this, two samples were used. The first was created artificially and contains an outlier. The second was formed on the basis of real economic data. In both cases, when normalizing the variables, the Pareto set turned out to be more representative than when working with non-normalized indicators. The example with an outlier illustrates the robustness of the least absolute deviations and the anti-robust ness of the ordinary least squares. It is shown how, based on the predicted values of the explained variable, it is possible to choose the optimal Pareto vertex.
Keywords: regression analysis; ordinary least squares; least absolute deviations; two-crite ria estimation; linear programming; robustness; Pareto set
For citation: Bazilevskiy M.P. Research of the two-criteria estimation method for line ar regression models. Digital models and solutions. 2024. Vol. 3, no. 4. Pp. 79–90. DOI: 10.29141/2949-477X-2024-3-4-5. EDN: GDLGKF.
