PA样本下密度核估计的相合性

CONSISTENCY OF DENSITY KERNEL ESTIMATION UNDER NEGATIVELY ASSOCIATED SAMPLE

设{Xi,i≥1}为同分布正相协(简记PA)随机变量序列,f(x)为X1的概率密度函数.基于样本X1,X2,…,Xn,在适当条件下证明了密度函数f(x)核估计的强相合及r阶矩相合.

Let {Xn,n>1} be a sequence of identically distributed and negatively associated (PA) variables with probability density function f(x).Based on PA samples,the kernel estimator of f(x) is studied.The rorder mean consistency and the strong consistency are shown under suitable conditions.