Before revision: Leading terms of conditional bias and variance are useful when we tend to investigate the mean-square properties of locally weighted polynomial regression. In this paper, we consider a geographically weighted regression model with any d-dimensional locations and M-dimensional subscripts. Under a given structure of dependence and assumption of stationarity, based on a weight matrixcontrolled by euclidean distance function with scale parameters , we analyze the leading terms of conditional bias, variance of locally weighted pool least square estimationin each location .
After revision: 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 leading terms of conditional bias, variance of locally weighted pool least square estimationin each location .