Open Access
2014 Time Scale in Least Square Method
Özgür Yeniay, Öznur İşçi, Atilla Göktaş, M. Niyazi Çankaya
Abstr. Appl. Anal. 2014: 1-6 (2014). DOI: 10.1155/2014/354237

Abstract

Study of dynamic equations in time scale is a new area in mathematics. Time scale tries to build a bridge between real numbers and integers. Two derivatives in time scale have been introduced and called as delta and nabla derivative. Delta derivative concept is defined as forward direction, and nabla derivative concept is defined as backward direction. Within the scope of this study, we consider the method of obtaining parameters of regression equation of integer values through time scale. Therefore, we implemented least squares method according to derivative definition of time scale and obtained coefficients related to the model. Here, there exist two coefficients originating from forward and backward jump operators relevant to the same model, which are different from each other. Occurrence of such a situation is equal to total number of values of vertical deviation between regression equations and observation values of forward and backward jump operators divided by two. We also estimated coefficients for the model using ordinary least squares method. As a result, we made an introduction to least squares method on time scale. We think that time scale theory would be a new vision in least square especially when assumptions of linear regression are violated.

Citation

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Özgür Yeniay. Öznur İşçi. Atilla Göktaş. M. Niyazi Çankaya. "Time Scale in Least Square Method." Abstr. Appl. Anal. 2014 1 - 6, 2014. https://doi.org/10.1155/2014/354237

Information

Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022210
MathSciNet: MR3193502
Digital Object Identifier: 10.1155/2014/354237

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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