UDC 519.852
APPLICATION OF PARAMETER ANTI-ROBUST ESTIMATION METHOD IN CONSTRUCTING LINEAR
REGRESSION WITH A GIVEN NUMBER OF ZERO ERRORS
S. I. Noskov, Dr. in technical sciences, full professor, Department of Information Systems and Information
Security, Irkutsk State Transport University, Irkutsk, Russia;
orcid.org/0000-0003-4097-2720, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
A. A. Butin, PhD (in physics and mathematics), associate professor, Department of Information Systems and
Information Security, Irkutsk State Transport University, Irkutsk, Russia;
orcid.org/0009-0007-7464-8810, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
S. V. Belyaev, assistant, Department of Information Systems and Information Security, Irkutsk State
Transport University, Irkutsk, Russia;
orcid.org/0009-0005-8824-9867, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
A linear regression construction method that minimizes maximum absolute approximation error for a
fixed number of observations with zero error has been developed. The task is reduced to linear Boolean programming: Boolean variables are introduced to indicate exact matches, and non-negative variables to represent errors. The equivalence of original and transformed problems is proved. A small penalty has been
added for the sum of error modules, eliminating ambiguity of solutions and guaranteeing a set number of
zero errors. The method was applied to Severstal's data for 2009-2021. The authors show that an increase in
the number of zero errors naturally increases the maximum error, and the sum of error modules does not
change monotonously. The proposed approach allows you to flexibly manage regression model properties.
Key words: linear regression, antirobastic estimation method, allowable set, equivalence.