Abstract

The material of this article is based on the author’s works devoted to the construction of the Pareto set in a two-criterion parameter estimation problem of the linear regression equation with the loss functions corresponding to urban and Chebyshev distances. It is known that the former is not sensitive to outliers, while the latter, in contrast, gravitates to them. In these works, it was shown that such a problem is reduced to a multicriteria linear programming problem and its solution is the Pareto set. This article proposes a method for checking whether an arbitrary parameter estimate meets the requirements of Pareto’s law and, in the case that it does not meet the requirements of Pareto’s law, determining the compromise estimates in the given senses. Moreover, all the problems formulated are reduced to computationally simple linear programming problems.

中文翻译：

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折衷线性回归参数的帕累托估计

摘要

本文的材料基于作者致力于在线性回归方程的双标准参数估计问题中构建帕累托集的工作，其中损失函数对应于城市和切比雪夫距离。众所周知，前者对异常值不敏感，而后者则相反。在这些工作中，表明这样的问题被简化为多准则线性规划问题，其解决方案是帕累托集。本文提出了一种检查任意参数估计是否满足帕累托定律要求的方法，在不满足帕累托定律要求的情况下，确定给定意义上的折衷估计。而且，