On Bandwidth Variation in Kernel Estimates-A Square Root Law
核估计中的带宽变化：平方根法则
We consider kernel estimation of a smooth density $f$ at a point, but depart from the usual approach in admitting an adaptive dependence of the sharpness of the kernels on the underlying density. Proportionally varying the bandwidths like $f^{-1/2}$ at the contributing readings lowers the bias to a vanishing fraction of the usual value, and makes for performance seen in well-known estimators that force moment conditions on the kernel (and so sacrifice positivity of the curve…