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

设X1,X2,…,Xn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）。

Suppose that X1,X2, ???,Xn 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).