摘要
In this paper,we present a detailed description of the limiting behaviorof local oscillation of the uniform empirical process.As an application,we estab-lish the laws of the iterated logarithm for the“naive”estimator and the nearestneighbor estimator of the density function.When compared to those of Hall andHong,the conditions of the bandwidth imposed here are as weak as possible.
In this paper,we present a detailed description of the limiting behaviorof local oscillation of the uniform empirical process.As an application,we estab-lish the laws of the iterated logarithm for the“naive”estimator and the nearestneighbor estimator of the density function.When compared to those of Hall andHong,the conditions of the bandwidth imposed here are as weak as possible.
基金
Research supported by National Natural Science Foundation of China
