  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.
