Geodesic
Compromise Pareto's evaluation of parameters linear regression
Matematičeskoe modelirovanie, Tome 32 (2020) no. 11, pp. 70-78

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The material in this article is based on the author’s works on the construction of the Pareto set in the two-criterion problem of estimating the parameters of a linear regression equation with loss functions corresponding to the city distance and Chebyshev distance. It is known that the first of them is insensitive to emissions, while the second, on the contrary, gravitates to them. In these works, it was shown that such a problem reduces to a multicriteria linear programming problem, and its solution is the Pareto set. The article proposes a method for verifying the Paretiness of an arbitrary parameter estimation, as well as, in the case of identifying its non-parity, determining compromises in the given meanings of the estimates. Moreover, all the formulated problems are reduced to computationally simple linear programming problems.
Keywords: linear regression, two-criteria parameter estimation, urban distance, Chebyshev distance, Pareto set of estimates, Pareto compromise estimates. 
@article{MM_2020_32_11_a5,
     author = {S. I. Noskov},
     title = {Compromise {Pareto's} evaluation of parameters linear regression},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {70--78},
     publisher = {mathdoc},
     volume = {32},
     number = {11},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2020_32_11_a5/}
}
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S. I. Noskov. Compromise Pareto's evaluation of parameters linear regression. Matematičeskoe modelirovanie, Tome 32 (2020) no. 11, pp. 70-78. http://geodesic.mathdoc.fr/item/MM_2020_32_11_a5/