On Nonparametric Kernel Density Estimates
本文提出不可容许核的概念，证明Epanechnikov型核是唯一可容许核，并给出两种减少偏差的新方法，同时提供Abramson平方根律的理论框架，以简化偏差和均方误差的计算。
The paper introduces the idea of inadmissible kernels and shows that an Epanechnikov type kernel is the only admissible kernel. An analysis of kernel density estimates leads to two new methods of bias reduction. We also discuss a general method of improving kernel density estimates in the sense of having smaller mean squared error. Finally we provide a theoretical framework for the operational method of using Abramson's square root law providing tangible and compact forms for the bias and mean squared error.