IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v175y2023ip1s0960077923008147.html
   My bibliography  Save this article

Applications of fractal interpolants in kernel regression estimations

Author

Listed:
  • Liu, Chiao-Wen
  • Luor, Dah-Chin

Abstract

Generating a function from its finite set of samples is widely studied in data fitting problems. The theory of nonparametric modeling has been developed by many researchers, and several types of estimators have been established in the literature. On the other hand, the fractal theory provides new technologies for making complicated curves and fitting experimental data, and fractal interpolation functions are established as generalizations of traditional interpolation techniques. The aim of this paper is to investigate applications of (smooth) fractal interpolation functions in nonparametric kernel regressions. We discuss a key sufficient condition in detail in the construction of (smooth) fractal interpolation functions. Then the Priestley–Chao estimator is considered, and we establish its fractal perturbation. The raw data we consider in our example is the Crude Oil WTI Futures daily highest price from 2021/10/13 to 2022/7/29. We take 11 samples from the raw data to construct a fractal perturbation of the Priestley–Chao regression function. SLSQP is applied to find the optimal values of hyperparameters so that the given empirical mean squared error is minimum. We see that nonparametric kernel regressions for finite sample data are widely used in applications, and we can decrease the empirical mean squared error further by considering fractal perturbations of these regression functions.

Suggested Citation

  • Liu, Chiao-Wen & Luor, Dah-Chin, 2023. "Applications of fractal interpolants in kernel regression estimations," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923008147
    DOI: 10.1016/j.chaos.2023.113913
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923008147
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113913?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Luor, Dah-Chin, 2020. "On the distributions of fractal functions that interpolate data points with Gaussian noise," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    2. Luor, Dah-Chin, 2018. "Fractal interpolation functions for random data sets," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 256-263.
    3. Tyada, K.R. & Chand, A.K.B. & Sajid, M., 2021. "Shape preserving rational cubic trigonometric fractal interpolation functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 866-891.
    4. Srijanani Anurag Prasad, 2021. "Super Coalescence Hidden-Variable Fractal Interpolation Functions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(03), pages 1-9, May.
    5. Viswanathan, P., 2022. "A revisit to smoothness preserving fractal perturbation of a bivariate function: Self-Referential counterpart to bicubic splines," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    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. Dai, Zhong & Liu, Shutang, 2023. "Construction and box dimension of the composite fractal interpolation function," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    2. Ri, Mi-Gyong & Yun, Chol-Hui, 2022. "Riemann-Liouville fractional derivatives of hidden variable recurrent fractal interpolation functions with function scaling factors and box dimension," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. Prasad, S.A. & Verma, S., 2023. "Fractal interpolation function on products of the Sierpiński gaskets," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    4. Luor, Dah-Chin, 2020. "On the distributions of fractal functions that interpolate data points with Gaussian noise," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).

    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:eee:chsofr:v:175:y:2023:i:p1:s0960077923008147. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.