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The Curve Estimation of Combined Truncated Spline and Fourier Series Estimators for Multiresponse Nonparametric Regression

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  • Helida Nurcahayani

    (Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia
    BPS—Statistics of Daerah Istimewa Yogyakarta Province, Bantul 55183, Indonesia)

  • I Nyoman Budiantara

    (Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia)

  • Ismaini Zain

    (Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia)

Abstract

Nonparametric regression becomes a potential solution if the parametric regression assumption is too restrictive while the regression curve is assumed to be known. In multivariable nonparametric regression, the pattern of each predictor variable’s relationship with the response variable is not always the same; thus, a combined estimator is recommended. In addition, regression modeling sometimes involves more than one response, i.e., multiresponse situations. Therefore, we propose a new estimation method of performing multiresponse nonparametric regression with a combined estimator. The objective is to estimate the regression curve using combined truncated spline and Fourier series estimators for multiresponse nonparametric regression. The regression curve estimation of the proposed model is obtained via two-stage estimation: (1) penalized weighted least square and (2) weighted least square. Simulation data with sample size variation and different error variance were applied, where the best model satisfied the result through a large sample with small variance. Additionally, the application of the regression curve estimation to a real dataset of human development index indicators in East Java Province, Indonesia, showed that the proposed model had better performance than uncombined estimators. Moreover, an adequate coefficient of determination of the best model indicated that the proposed model successfully explained the data variation.

Suggested Citation

  • Helida Nurcahayani & I Nyoman Budiantara & Ismaini Zain, 2021. "The Curve Estimation of Combined Truncated Spline and Fourier Series Estimators for Multiresponse Nonparametric Regression," Mathematics, MDPI, vol. 9(10), pages 1-22, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1141-:d:557214
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    References listed on IDEAS

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    1. Made Ayu Dwi Octavanny & I. Nyoman Budiantara & Heri Kuswanto & Dyah Putri Rahmawati, 2020. "Nonparametric Regression Model for Longitudinal Data with Mixed Truncated Spline and Fourier Series," Abstract and Applied Analysis, Hindawi, vol. 2020, pages 1-11, December.
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    5. Ni Putu Ayu Mirah Mariati & I. Nyoman Budiantara & Vita Ratnasari & Viliam Makis, 2020. "Combination Estimation of Smoothing Spline and Fourier Series in Nonparametric Regression," Journal of Mathematics, Hindawi, vol. 2020, pages 1-10, July.
    6. Jaehee Kim & Jeffrey Hart, 2011. "A change-point estimator using local Fourier series," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 83-98.
    7. Victor Lapshin, 2019. "A Nonparametric Approach to Bond Portfolio Immunization," Mathematics, MDPI, vol. 7(11), pages 1-12, November.
    8. Zhao, Ge & Ma, Yanyuan, 2016. "Robust nonparametric kernel regression estimator," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 72-79.
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    1. Lilis Laome & I Nyoman Budiantara & Vita Ratnasari, 2022. "Estimation Curve of Mixed Spline Truncated and Fourier Series Estimator for Geographically Weighted Nonparametric Regression," Mathematics, MDPI, vol. 11(1), pages 1-13, December.

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