Bandwidth Choice for Average Derivative Estimation
研究了核估计中平均导数的带宽选择问题，通过渐近分析找到优化带宽的表达式，并指出高维时需用负核以避免偏差主导，最后用经济学需求法则例子验证理论。
The average derivative is the expected value of the derivative of a regression function. Kernel methods have been proposed as a means of estimating this quantity. The problem of bandwidth selection for these kernel estimators is addressed here. Asymptotic representations are found for the variance and squared bias. These are compared with each other to find an insightful representation for a bandwidth optimizing terms of lower order than n-1. It is interesting that, for dimensions greater than 1, negative kernels have to be used to prevent domination of bias terms in the asymptotic expression of the mean squared error. The extent to which the theoretical conclusions apply in practice is investigated in an economical example related to the so-called "law of demand."