A simple test for spatial heteroscedasticity in spatially varying coefficient models

Abstract

In spatially varying coefficient models, there has been a common assumption of homoscedasticity. In many practical situations, however, rarely can we know a priori whether this assumption is true or not. In this paper, we propose a simple test for detecting spatial heteroscedasticity in spatially varying coefficient models. Specifically, the testing procedure is constructed based on the square root of the absolute value of the residuals obtained by the local linear geographically weighted estimation. Simulation experiments are conducted to evaluate the performance of the proposed method and the results demonstrate that the method in the paper is quite robust to the types of the error distributions and is more powerful in some cases, especially when the sample size is not very large. A real-world data set is analyzed to demonstrate the application of the proposed test method and the paper is ended with a final remark.

Keywords:

• Spatially varying coefficient models
• local linear geographically weighted regression
• spatial heteroscedasticity

Acknowledgments

This research is supported by the National Natural Science Foundations of China (No. 11601126, No. 11326181) and the Student Research Training Program of Henan University of Science and Technology (No. 2020178). The authors are especially grateful to the reviewer for his valuable comments and suggestions which lead to significant improvements on the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is supported by the National Natural Science Foundations of China (No. 11601126, No. 11326181) and the Student Research Training Program of Henan University of Science and Technology (No. 2020178).