NQD样本最近邻密度估计的一致强相合速度

Rate of uniform strong consistency of nearest neighbor estimator of density function for pariwise NQD samples

设X1,X2,…,X n是同分布的两两NQD样本,具有相同的密度函数f(x),利用两两NQD序列的Bernstein型不等式,将负相关(NA)样本的最近邻密度估计的一致强相合速度推广到两两NQD样本,在更弱的条件下,获得了与NA样本情形下相同的结论。

It is supposed that X1, X2,…, Xn are independent and identically distributed pariwise NQD samples, with a common density functionf（x）. By using the Bernstein type inequality for pariwise NQD sequences, the rate of uniform strong con- sistency of nearest neighbor estimator of density function for negatively associated （NA） samples is extended to parlwise NQD sam- ples. Under much weaker conditions, the results are as good as the corresponding ones for NA samples.