On Estimation of Parameters of a Three-Dimensional Uniform Regression Model

УДК 519.87

Abstract

Typically, a researcher faces computational difficulties in assessing the parameters of a certain model when modeling the relationship between different indicators of analysis. A suitable model is generally obtained by a sequential refinement of the features included in its composition and, therefore, by performing multiple repetitions of computational algorithms. At the same time, the computational complexity of these algorithms begins to play a significant role in modeling. A certain set of indicators is used to reduce the number of iterations. These indicators are responsible for the quality of the constructed model and capable of “signaling" about the need to adjust the model. The model parameters and the quality functional value are such indicators in regression modeling. They are able to answer the question of the appropriateness of building a particular model and are indicators of the quality of the resulting functional dependence.

In this paper, we study methods and algorithms for constructing and evaluating the main indicators of L_∞-regression — a quality indicator and model parameters. The first part of the paper describes the most efficient computational procedures for determining parameters in the case of a three-dimensional uniform regression model, indicates the complexity of these algorithms, and gives a geometric interpretation. In the second part of the paper, a series of theorems on estimating the values of the parameters of threedimensional L_∞-regression is presented, and a formula for calculation of an indicator of sample uniformity is provided.