Research of the two-criteria estimation method for linear regression models
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 programm...
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| Format: | Article |
| Language: | English |
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Ural State University of Economics
2025-01-01
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| Series: | Цифровые модели и решения |
| Subjects: | |
| Online Access: | http://usue-journal.ru/en/issues-2024/70-anglijskij-yazyk/tsmiren/11/524-research-of-the-two-criteria-estimation-method-for-linear-regression-models |
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| _version_ | 1841556393546481664 |
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| author | M.P. Bazilevskiy |
| author_facet | M.P. Bazilevskiy |
| author_sort | M.P. Bazilevskiy |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f5a16c256f71479a92e1fab709dfd65e |
| institution | Kabale University |
| issn | 2949-477X 2782-4934 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Ural State University of Economics |
| record_format | Article |
| series | Цифровые модели и решения |
| spelling | doaj-art-f5a16c256f71479a92e1fab709dfd65e2025-01-07T09:11:57ZengUral State University of EconomicsЦифровые модели и решения2949-477X2782-49342025-01-0134799010.29141/2949-477X-2024-3-4-5Research of the two-criteria estimation method for linear regression modelsM.P. Bazilevskiy 0Irkutsk State Transport University, Irkutsk, Russian FederationThe 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.http://usue-journal.ru/en/issues-2024/70-anglijskij-yazyk/tsmiren/11/524-research-of-the-two-criteria-estimation-method-for-linear-regression-modelsregression analysisordinary least squaresleast absolute deviationstwo-crite ria estimationlinear programmingrobustnesspareto set |
| spellingShingle | M.P. Bazilevskiy Research of the two-criteria estimation method for linear regression models Цифровые модели и решения regression analysis ordinary least squares least absolute deviations two-crite ria estimation linear programming robustness pareto set |
| title | Research of the two-criteria estimation method for linear regression models |
| title_full | Research of the two-criteria estimation method for linear regression models |
| title_fullStr | Research of the two-criteria estimation method for linear regression models |
| title_full_unstemmed | Research of the two-criteria estimation method for linear regression models |
| title_short | Research of the two-criteria estimation method for linear regression models |
| title_sort | research of the two criteria estimation method for linear regression models |
| topic | regression analysis ordinary least squares least absolute deviations two-crite ria estimation linear programming robustness pareto set |
| url | http://usue-journal.ru/en/issues-2024/70-anglijskij-yazyk/tsmiren/11/524-research-of-the-two-criteria-estimation-method-for-linear-regression-models |
| work_keys_str_mv | AT mpbazilevskiy researchofthetwocriteriaestimationmethodforlinearregressionmodels |