Under the realization that Geographically Weighted Regression (GWR) is a data-borrowing technique, this paper derives expressions for the amount of bias introduced to local parameter estimates by borrowing data from locations where the processes might be different from those at the regression location. This is done for both GWR and Multiscale GWR (MGWR). We demonstrate the accuracy of our expressions for bias through a comparison with empirically derived estimates based on a simulated dataset with known local parameter values. By being able to compute the bias in both models we are able to demonstrate the superiority of MGWR. We then demonstrate the utility of a corrected Akaike Information Criterion statistic in finding optimal bandwidths in both GWR and MGWR as a trade-off between minimizing both bias and uncertainty. We further show how bias in one set of local parameter estimates can affect the bias in another set of local estimates. The bias derived from borrowing data from other locations appears to be very small.

在认识到地理加权回归（GWR）是一种数据借阅技术的情况下，本文通过从过程可能与回归位置不同的位置借入数据来导出引入局部参数估计的偏差量的表达式。这对于GWR和Multiscale GWR（MGWR）都是完成的。通过与基于已知局部参数值的模拟数据集根据经验得出的估计值进行比较，我们证明了偏差表达的准确性。通过能够在两个模型中计算偏差，我们可以证明MGWR的优越性。然后，我们证明了校正的Akaike信息准则统计量在寻找GWR和MGWR中的最佳带宽方面的实用性，作为在最小化偏差和不确定性之间的权衡。我们进一步展示了一组局部参数估计中的偏差如何影响另一组局部估计中的偏差。从其他位置借用数据所产生的偏差似乎很小。