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Mixed Spline Smoothing and Kernel Estimator in Biresponse Nonparametric Regression

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  • Dyah P. Rahmawati
  • I. N. Budiantara
  • Dedy D. Prastyo
  • Made A. D. Octavanny

Abstract

Mixed estimators in nonparametric regression have been developed in models with one response. The biresponse cases with different patterns among predictor variables that tend to be mixed estimators are often encountered. Therefore, in this article, we propose a biresponse nonparametric regression model with mixed spline smoothing and kernel estimators. This mixed estimator is suitable for modeling biresponse data with several patterns (response vs. predictors) that tend to change at certain subintervals such as the spline smoothing pattern, and other patterns that tend to be random are commonly modeled using kernel regression. The mixed estimator is obtained through two‐stage estimation, i.e., penalized weighted least square (PWLS) and weighted least square (WLS). Furthermore, the proposed biresponse modeling with mixed estimators is validated using simulation data. This estimator is also applied to the percentage of the poor population and human development index data. The results show that the proposed model can be appropriately implemented and gives satisfactory results.

Suggested Citation

  • Dyah P. Rahmawati & I. N. Budiantara & Dedy D. Prastyo & Made A. D. Octavanny, 2021. "Mixed Spline Smoothing and Kernel Estimator in Biresponse Nonparametric Regression," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2021(1).
    • Handle: RePEc:wly:jijmms:v:2021:y:2021:i:1:n:6611084
    DOI: 10.1155/2021/6611084
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    References listed on IDEAS

    as
    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.
    2. Okumura, Hidenori & Naito, Kanta, 2006. "Non-parametric kernel regression for multinomial data," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 2009-2022, October.
    3. Stephen G. GRUBAUGH, 2015. "Economic Growth And Growth In Human Development," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 15(2), pages 5-16.
    4. 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, John Wiley & Sons, vol. 2020(1).
    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.
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