Comparison and Extension of Nonparametric Regression and Nonparametric-GWR when used as a Spatial Predictor
Sifriyani Sifriyani [a*], I Nyoman Budiantara [b], Krishna Purnawan Candra [c], Syaripuddin [d], Wiwit Pura Nurmayanti [a], Nariza Wanti Wulan Sari [a], Ratna Kusuma [e], and Raudhatul Jannah [f]

[a] Study Program of Statistics, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Mulawarman University, Samarinda 75119 Indonesia
[b] Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111 Indonesia
[c] Department of Agriculture, Faculty of Wet Tropical Agriculture, Mulawarman University, Samarinda 75119 Indonesia
[d] Study Program of Mathematics, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Mulawarman University, Samarinda 75119 Indonesia
[e] Study Program of Biology, Department of Biology, Faculty of Mathematics and Natural Sciences, Mulawarman University, Samarinda 75119 Indonesia
[f] Student of Statistics Study Program, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Mulawarman University, Samarinda 75119 Indonesia

Abstract

In this study, comparison and extension of nonparametric regression models and geographically weighted nonparametric regression with truncated spline approach. Geographically Weighted Spline Nonparametric Regression (GWSNR) is a combination of nonparametric truncated spline regression with Geographically Weighted Regression (GWR) as a development of nonparametric regression on spatial data when the regression curve is unknown. GWSNR combines the spatial properties of GWR with nonparametric truncated spline regression that allows the model to capture local variations in the relationship between variables at various locations. The nonparametric regression component uses a truncated spline estimator and uses weighted kernel function of bisquare and Gaussian. The selection of the best weighted function is based on the minimum Generalized Cross Validation (GCV) value. The case study in this study is rice productivity based on 34 Provinces in Indonesia. The results showed the best GWSNR model using Gaussian kernel function weighted with minimum GCV value and optimal number of knot points.

Keywords: Spatial Statistics, Nonparametric Regression, Nonparametric-GWR, Spline, Statistical Modeling

Topic: Statistics