独立样本最近邻密度估计的强相合速度

The Rate of Strong Consistency of Nearest Neighbor Density Estimator for Independent Samples

摘要: 设X₁,X₂,…,X_n是独立同分布样本,具有共同的密度函数 f（x）.在f（x）满足适当的条件下给出最近邻密度估计的强相合收敛速度,其速度可达到O（n^-1/3（log n）^1/3）。

Abstract: Suppose that X₁,X₂,…,X_n are i.i.d. samles, with a common density function f（x）. This paper gives that the rate of the strong consistency of nearest neighbor density estimator under some suitable conditions. This rate can get O（n^-1/3（logn）^1/3）.