The commonly used Geographically Weighted Regression (GWR) fitting method for a spatial varying coefficient model is to select a bandwidth h for the geographic location (u, v), and assign the same weight to the two dimensions. However, spatial data usually present anisotropy. The introduction of a two-dimensional bandwidth matrix not only gives weight from two dimensions separately, but also increases the direction of kernel smoothness. The adaptive bandwidth matrix is more flexible. Therefore, in this paper, a two dimensional bandwidth matrix is introduced into the spatial varying coefficient model for parameter estimation. Through simulation experiments, the results obtained under the adaptive bandwidth matrix are compared with those obtained under the global bandwidth matrix, indicating the effectiveness of introducing the adaptive bandwidth matrix.

中文翻译：

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空间变系数模型中带宽矩阵的选择以检测各向异性回归关系

空间变系数模型常用的地理加权回归 (GWR) 拟合方法是为地理位置 ( u , v)，并为两个维度分配相同的权重。然而，空间数据通常呈现各向异性。二维带宽矩阵的引入不仅从两个维度分别给出权重，而且增加了核平滑的方向。自适应带宽矩阵更加灵活。因此，本文在空间变系数模型中引入二维带宽矩阵进行参数估计。通过仿真实验，将自适应带宽矩阵下的结果与全局带宽矩阵下的结果进行比较，表明引入自适应带宽矩阵的有效性。