摘要翻译：
众所周知，地理加权回归(GWR)与变系数模型本质上是相同的。在以往的变系数模型研究中，学者们倾向于使用基于多维核的局部加权估计(MLWE)，从而考虑了距离和方向的信息。然而，在构造地理加权估计的局部权重矩阵时，相邻位置之间的距离是控制权重矩阵条目值的唯一因素。也就是说，GWR的估计是基于距离核的。因此，本文在具有多维下标的平稳和有限相依数据下，在不假定系数函数形式的情况下，分析了Mlwe的局部均方性质，并与Mlwe进行了比较。理论和仿真结果表明，地理加权局部线性估计(GWLE)比MLWE具有更高的渐近效率。此外，还得到了最佳带宽与尺度参数选择和设计之间的关系。
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英文标题：
《An Note on Why Geographically Weighted Regression Overcomes
  Multidimensional-Kernel-Based Varying-Coefficient Model》
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作者：
Zihao Yuan
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最新提交年份：
2018
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分类信息：

一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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英文摘要：
  It is widely known that geographically weighted regression(GWR) is essentially same as varying-coefficient model. In the former research about varying-coefficient model, scholars tend to use multidimensional-kernel-based locally weighted estimation(MLWE) so that information of both distance and direction is considered. However, when we construct the local weight matrix of geographically weighted estimation, distance among the locations in the neighbor is the only factor controlling the value of entries of weight matrix. In other word, estimation of GWR is distance-kernel-based. Thus, in this paper, under stationary and limited dependent data with multidimensional subscripts, we analyze the local mean squared properties of without any assumption of the form of coefficient functions and compare it with MLWE. According to the theoretical and simulation results, geographically-weighted locally linear estimation(GWLE) is asymptotically more efficient than MLWE. Furthermore, a relationship between optimal bandwith selection and design of scale parameters is also obtained.
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PDF链接：
https://arxiv.org/pdf/1803.01402