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Estimation Curve of Mixed Spline Truncated and Fourier Series Estimator for Geographically Weighted Nonparametric Regression

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  • Lilis Laome

    (Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia
    Department of Statistics, Faculty of Mathematics and Natural Sciences, Universitas Halu Oleo, Kendari 93132, Indonesia)

  • I Nyoman Budiantara

    (Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia)

  • Vita Ratnasari

    (Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia)

Abstract

Geographically Weighted Regression (GWR) is the development of multiple linear regression models used in spatial data. The assumption of spatial heterogeneity results in each location having different characteristics and allows the relationships between the response variable and each predictor variable to be unknown, hence nonparametric regression becomes one of the alternatives that can be used. In addition, regression functions are not always the same between predictor variables. This study aims to use the Geographically Weighted Nonparametric Regression (GWNR) model with a mixed estimator of truncated spline and Fourier series. Both estimators are expected to overcome unknown data patterns in spatial data. The mixed GWNR model estimator is then determined using the Weighted Maximum Likelihood Estimator (WMLE) technique. The estimator’s characteristics are then determined. The results of the study found that the estimator of the mixed GWNR model is an estimator that is not biased and linear to the response variable y.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:152-:d:1017922
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    References listed on IDEAS

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    1. Dziauddin, Mohd Faris, 2019. "Estimating land value uplift around light rail transit stations in Greater Kuala Lumpur: An empirical study based on geographically weighted regression (GWR)," Research in Transportation Economics, Elsevier, vol. 74(C), pages 10-20.
    2. 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.
    3. Sifriyani Sifriyani, 2019. "Simultaneous Hypothesis Testing of Multivariable Nonparametric Spline Regression in the GWR Model," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(4), pages 32-46, July.
    4. 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.
    5. Jinjun Tang & Fan Gao & Fang Liu & Wenhui Zhang & Yong Qi, 2019. "Understanding Spatio-Temporal Characteristics of Urban Travel Demand Based on the Combination of GWR and GLM," Sustainability, MDPI, vol. 11(19), pages 1-19, October.
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