IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2014y2014i1n354237.html

Time Scale in Least Square Method

Author

Listed:
  • Özgür Yeniay
  • Öznur İşçi
  • Atilla Göktaş
  • M. Niyazi Çankaya

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.

Suggested Citation

  • Özgür Yeniay & Öznur İşçi & Atilla Göktaş & M. Niyazi Çankaya, 2014. "Time Scale in Least Square Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:354237
    DOI: 10.1155/2014/354237
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/354237
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/354237?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Martin Bohner & Allan Peterson, 2001. "Dynamic Equations on Time Scales," Springer Books, Springer, number 978-1-4612-0201-1, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jan Čermák & Tomáš Kisela & Luděk Nechvátal, 2011. "Discrete Mittag‐Leffler Functions in Linear Fractional Difference Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    2. J. Diblík & M. Růžičková & Z. Šmarda & Z. Šutá, 2012. "Asymptotic Convergence of the Solutions of a Dynamic Equation on Discrete Time Scales," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Qiaoshun Yang & Lynn Erbe & Baoguo Jia, 2014. "Oscillation of Certain Emden‐Fowler Dynamic Equations on Time Scales," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Monika Dryl & Delfim F. M. Torres, 2014. "Necessary Condition for an Euler‐Lagrange Equation on Time Scales," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Hsuan-Ku Liu, 2012. "Application of the Variational Iteration Method to Strongly Nonlinear q‐Difference Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    6. Ling Wu & Jiang Zhu, 2013. "Fractional Cauchy Problem with Riemann‐Liouville Derivative on Time Scales," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    7. Li Gao & Quanxin Zhang & Shouhua Liu, 2014. "New Oscillatory Behavior of Third‐Order Nonlinear Delay Dynamic Equations on Time Scales," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    8. Shurong Sun & Martin Bohner & Shaozhu Chen, 2010. "Weyl‐Titchmarsh Theory for Hamiltonian Dynamic Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    9. Zhenlai Han & Tongxing Li & Shurong Sun & Chao Zhang & Bangxian Han, 2011. "Oscillation Criteria for a Class of Second‐Order Neutral Delay Dynamic Equations of Emden‐Fowler Type," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    10. Pavel Řehák, 2011. "Asymptotic Behavior of Solutions to Half‐Linear q‐Difference Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    11. Hsuan-Ku Liu, 2013. "Developing a Series Solution Method of q‐Difference Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    12. Liangji Sun & Chengyan Liu & Xiaodi Li, 2014. "Practical Stability of Impulsive Discrete Systems with Time Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    13. Hong-Cun Zhai, 2013. "A Note on Certain Modular Equations about Infinite Products of Ramanujan," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    14. Qinghua Feng & Fanwei Meng & Yaoming Zhang & Jinchuan Zhou & Bin Zheng, 2012. "Some Delay Integral Inequalities on Time Scales and Their Applications in the Theory of Dynamic Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    15. Yuangong Sun, 2011. "Interval Oscillation Criteria for Second‐Order Dynamic Equations with Nonlinearities Given by Riemann‐Stieltjes Integrals," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    16. Chao Wang & Ravi P. Agarwal, 2014. "A Further Study of Almost Periodic Time Scales with Some Notes and Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    17. Kanit Mukdasai & Piyapong Niamsup, 2011. "An LMI Approach to Stability for Linear Time‐Varying System with Nonlinear Perturbation on Time Scales," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    18. M. Zakarya & Ghada AlNemer & H. A. Abd El-Hamid & Roqia Butush & H. M. Rezk, 2022. "On Refinements of Multidimensional Inequalities of Hardy‐Type via Superquadratic and Subquadratic Functions," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    19. Sung Kyu Choi & Yoon Hoe Goo & Namjip Koo, 2008. "h‐Stability of Dynamic Equations on Time Scales with Nonregressivity," Abstract and Applied Analysis, John Wiley & Sons, vol. 2008(1).
    20. Yan Sun & Yongping Sun & Patricia J. Y. Wong, 2014. "New Results for Multipoint Singular Boundary Value Problems on a Measure Chain," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:354237. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.