一个连续时间非平稳随机过程下的核密度估计的最优收敛速度

The Convergence Rate of a Density Kernel Estimatorfor a Nonstationary Continuous Time Stochastic Process

设{Xt,t≥0}为定义在Rd上的随机过程,它由模型Xt＝zt+φ(Yt)+ εt 确定,{Yt} 和{εt}相互独立,而zt为非随机变量．对于连续观察的样本,本文给出了非参数密度核估计极其在均方意义下的最优收敛速度,并讨论了非随机项运动形式对此速度的影响．

Let {Xt,t≥0} be a stochastic process taking values in Rd and defined by the model Xt = zt + φ(Yt) + εt,{Yt} and {εt} are independent stochastic processes, zt is a deterministic function of time. We dealt with theasymptotic behavior of the nonparametric density estimator in quadratic error sense. That is, the consistency and the optimal rate of it, emphasizing on the effect by the behavior of zt, which is convergent al1d periodicrespective1y.