Paired piecewise linear regression model with fixed nodes
- Authors: Zubrilin K.M.1
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Affiliations:
- Branch of Federal State Budgetary Educational Institution of Higher Education «Kerch State Maritime Technological University» in Feodosiya
- Issue: Vol 60, No 4 (2024)
- Pages: 113-124
- Section: Mathematical analysis of economic models
- URL: https://journal-vniispk.ru/0424-7388/article/view/269451
- DOI: https://doi.org/10.31857/S0424738824040103
- ID: 269451
Open Access
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Abstract
In this paper we develop a method for constructing a paired regression model in the class of piecewise linear continuous functions with fixed nodes. The concept of linear division of the correlation field, its partial sections and its nodes is introduced into consideration. Using the linear division of the correlation field, a class of piecewise linear functions with fixed nodes is determined. The linear division is revealed during the visual analysis of the correlation field. Using the least squares method, a system of linear equations is compiled to find point estimates of the parameters of the approximating function. With the exception of two unknown angular coefficients (unknown) this system is reduced to a tridiagonal system of equations, the unknowns of which are the nodal values of the approximating function. The tridiagonal system is solved by the run-through method. An algorithm was constructed to demonstrate the operation of the developed method. Its initial data is arrays of the corresponding values of the explanatory and dependent variables, as well as an array of numbers of the right ends of the intervals defining the nodes. An array of fixed nodes is constructed from an array of values of the explanatory variable and an array of numbers of the right ends of the intervals. Next, an array of point estimates of the parameters of the approximating function is constructed. This algorithm is implemented in Python in the form of user-defined functions.
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About the authors
K. M. Zubrilin
Branch of Federal State Budgetary Educational Institution of Higher Education «Kerch State Maritime Technological University» in Feodosiya
Author for correspondence.
Email: kzubrilin@yandex.ru
Russian Federation, Feodosiya
References
- Боровской И. Г., Костелей Я. В. (2017). Прогнозная модель финансовых рядов на основе кусочно-линейной аппроксимации // Доклады ТУСУРа. Т. 20. № 2. С. 73–75. [Borovskoy I. G., Kosteley Y. V. (2017). Use of piecewise-linear approximation to identify trends in the financial market. Proceedings of TUSUR University, 20, 2, 73–75 (in Russian).]
- Иванова Н. К., Лебедева С. А., Носков С. И. (2016). Идентификация параметров некоторых негладких регрессий // Информационные технологии и проблемы математического моделирования в управлении сложными системами. № 17. С. 107–110. [Ivanova N. K., Lebedeva S. A., Noskov S. I. (2016). Identification of parameters of some nonsmooth regressions. Information Technologies and Problems of Mathematical Modeling in the Management of Complex Systems in the Management of Complex Systems, 7, 107–110 (in Russian).]
- Ильин В. П., Кузнецов Ю. И. (1985). Трехдиагональные матрицы и их приложения. Москва: Наука. [Ilyin V. P., Kuznetsov Yu.I. (1985). Tridiagonal matrices and their applications. Moscow: Nauka (in Russian).]
- Носков С. И. (2013). Оценивание параметров аппроксимирующей функции с постоянными пропорциями // Современные технологии. Системный анализ. Моделирование. № 2. С. 135–136. [Noskov S. I. (2013). Estimation of parameters of the approximating function with constant proportions. Modern Technologies. System Analysis. Modeling, 2, 135–136 (in Russian).]
- Носков С. И. (2023). Подход к формализации вложенной кусочно-линейной регрессии // Международный журнал гуманитарных и естественных наук. № 1–2 (76). С. 218–220. [Noskov S. I. (2023). Approach to formalizing nested piece-linear regression. International Journal of Humanities and Natural Sciences, 1–2 (76), 218–220 (in Russian).]
- Носков С. И., Лоншаков Р. В. (2008). Идентификация параметров кусочно-линейной регрессии // Информационные технологии и проблемы математического моделирования в управлении сложными системами. № 6. С. 63–64. [Noskov S. I., Lonshakov R. V. (2008). Identification of parameters of piecewise linear regression. Information Technologies and Problems of Mathematical Modeling in the Management of Complex Systems, 6, 63–64 (in Russian).]
- Носков С. И., Хоняков А. А. (2019). Программный комплекс построения некоторых типов кусочно-линейных регрессий // Информационные технологии и математическое моделирование в управлении сложными системами. № 3. С. 47–55. [Noskov S. I., Khonyakov A. A. (2019). A software package for constructing some types of piecewise linear regressions. Information Technologies and Mathematical Modeling in the Management of Complex Systems, 3, 47–55 (in Russian).]
