α-混合随机序列最近邻密度估计的强相合收敛速度

The Rate of Strong Consistency Convergence of Nearest Neighbor Density Estimator forα-mixing Sequence

设{X_i)_(i=1)~∞是一维平稳序列,具有公共的未知密度f(x),在(X_i)_(i=1)~∞是α-混合的条件下,给出了f(x)基于前n个观测值{X_i)_(i=1)~n的最近邻密度估计的强相合收敛速度,当f(x)满足适当条件,收敛速度可达到o(n^(-1/3)(ln n)^(4(1+ρ)/3))).

Suppose that {Xi}i=1^∞ is a stationarity random sequence with a common unknown density function f（x）. It is assumed that {Xi}i=1^∞is a sequence of α- mixing, we give a strong consistency convergence rate of the neighbor density estimator for f（x）, which is based on the first n observed value. Under some conditions, this rate can arrive 0（n^-1/3（ln n）^4（1＋p）/3））.