THE SECOND ORDER NESTING FOR HOMOGENEOUS PIECEWISE LINEAR REGRESSION OF THE FIRST TYPE

The authors of the paper provide a brief overview of publications related to the construction and analysis of nested model forms of various orders in mathematical modeling of various objects. In particular, the following items are considered: multivariate approximation of the Taylor series for the logarithm of the integrand in the study of nested random effects models, a general and scalable method for studying the influence of nested structures in higher-order interactions under group cooperation, a nested adaptive control scheme for the sliding mode of an integral terminal for uncertain high-order nonlinear systems, a new approach to modeling aerodynamic nonlinearities in the time domain using an artificial neural network framework with a nested cellular automata scheme, and a doubly nested unbalanced data panel. The authors set the task of developing an algorithm for identifying the parameters of a homogeneous piecewise linear regression of the first type with the second order of nesting for the case when the loss function is the sum of the calculated and actual values of the dependent variable, corresponding to the least absolute value method. It is shown that this method can be based on reducing the given problem to a linear-Boolean programming problem. A numerical example is solved.