APPLICATION OF THE MIXED PARAMETER ESTIMATION METHOD IN THE CONSTRUCTION OF A HOMOGENEOUS NESTED PIECEWISE LINEAR REGRESSION OF THE FIRST TYPE
Abstract
The paper is devoted to the development of an algorithm for identifying the parameters of a homogeneous nested piecewise linear regression of the first type – a model that is in demand when analyzing complex systems whose behavior cannot be adequately described by smooth functions. The review part of the work systematizes modern publications illustrating the use of piecewise linear forms in various subject areas: from modeling energy consumption and nonlinear control systems to image processing, reconstruction of genetic networks, and filtering of geophysical data. The novelty of the study lies in the fact that for the first time for this class of models an identification algorithm based on the mixed estimation method (MEM) is proposed, which allows flexible combination of two different quality criteria. It is shown that by introducing additional Boolean variables and auxiliary constraints, the original optimization problem is reduced to a standard linear Boolean programming problem, which makes it possible to use available numerical methods for its solution. The effectiveness of the developed algorithm is demonstrated on real data of the mining and metallurgical company Norilsk Nickel for 2010–2024. The dependent variable is revenue, and the predictors are the production volumes of nickel, palladium, copper and platinum. Two alternative models are constructed – using the classical least absolute deviations method and the proposed mixed estimation method. A comparative analysis shows that the second model has a slightly higher average percentage error, but significantly outperforms in the magnitude of the maximum error on the control subsample, which makes it preferable in conditions where outliers are critical. The results obtained confirm the practical value of MEM for constructing interpretable and robust regression dependencies
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