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WEIGHTED MAXIMUM CONSISTENCY METHOD IN REGRESSION ANALYSIS
Keywords:
regression model, loss function, behavior consistency criterion, maximum consistency method, linear-Boolean programming problem, weights of pairs of observations.DOI:
https://doi.org/10.17654/0972361722030Abstract
The work is based on the maximum consistency method (MCM) in regression analysis developed by S. I. Noskov. Unlike traditional methods for regression analysis, which are based on minimizing error-dependent approximation of loss functions, MCM is based on maximizing the number of coincidences of the increments of the actual and calculated values of the dependent variable of the model for all pairs of observations of the sample. The implementation of MCM is reduced to solving the linear-Boolean programming (LBP) problem. The use of MCM is especially important when developing regression models designed to solve a wide range of predictive tasks, in which it is necessary not so much to accurately calculate the future values of dependent variables (although, of course, this is very important), as to correctly predict the signs of their increments, for example, when planning operations on commodity, stock and currency exchanges. In this paper, a modification of the MCM - weighted maximum consistency method (WMCM) is proposed, which assumes either the assignment of positive weights for all pairs of observation numbers of the sample, or the formation of a set of pairs of numbers for which achieving this consistency is especially necessary. Each of these two methods reduces to the corresponding transformation of the objective function in the LBP problem.
Received: January 21, 2022
Accepted: February 22, 2022
References
E. Z. Demidenko, Linear and non-linear regressions, Finance and Statistics, Moscow, 1981, 302 pp. (in Russian).
S. I. Noskov, Generalized criterion of coordination of behavior in regression analysis, Information Technology and Mathematical Modeling in the Management of Complex Systems: Electronic Scientific Journal 1(1) (2018), 14-20.
S. I. Noskov, Maximum consistency method in regression analysis, Bulletin of the Tula State University. Technical Science 10 (2021), 380-385.
S. I. Noskov and A. S. Vergasov, Maximization of the dynamic criterion of consistency of behavior as a partially Boolean linear programming problem, Advances and Applications in Discrete Mathematics 29(1) (2022), 25-40.
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