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

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.

Automated summary

Geographically Weighted Regression (GWR) is a spatial data analysis method that uses multiple linear regression models. The assumption of spatial heterogeneity results in different characteristics for each location, making the relationships between the response variable and predictor variables unknown. Nonparametric regression is used as an alternative method to address this issue. This study introduces a Geographically Weighted Nonparametric Regression (GWNR) model with a mixed estimator of truncated spline and Fourier series. The estimator, determined using the Weighted Maximum Likelihood Estimator (WMLE) technique, is unbiased and shows a linear relationship with the response variable.