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.

在空间变化的系数模型中，一直存在均等的假设。但是，在许多实际情况下，我们很少能先验地知道这个假设是否正确。在本文中，我们提出了一种在空间变化系数模型中检测空间异方差的简单测试。具体地，基于通过局部线性地理加权估计获得的残差的绝对值的平方根来构造测试过程。仿真实验对所提方法的性能进行了评估，结果表明本文方法对误差分布的类型具有较强的鲁棒性，在某些情况下更有效，尤其是在样本量不是很大的情况下。