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 . Furthermore, according to mean integrated squared error, we demonstrate how the design of scale parameters affect the value of globally optimal bandwith .
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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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
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
R
leading terms of conditional bias, variance of locally weighted pool least square estimationin each location
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
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according to mean integrated squared error, we demonstrate how the
a relationship between optimal bandwith selection and
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affect the value of globally optimal bandwith
is also obtained