设X1,X2,…,Xn是同分布的负相依(ND)样本,具有共同的密度函数f(x),利用相应的Bernstein不等式,将负相关(NA)样本最近邻密度估计的一致强相合性推广到ND样本,得到其最近邻密度估计的一致强相合性.
Suppose that X1,X2,…,Xn are negative dependent(ND) samples,with a common density function f(x).By the use of the corresponding Bernstein inequality,the uniform strong consistency of nearest neighbor estimator of density function for negatively associated(NA) samples is extended to ND samples,and the latter uniform strong consistency of nearest neighbor estimator of density function is obtained.