未知方向密度估计的收敛率

摘要

Motivated by recent work on exploratory projection pursuit,we give the kernel estimator of density on an unknown projection orientation θ0(‖θ0‖=1) by combining the estimator ofθ0 with classical kernel estimation and obtain its asymptotically normality at a fixed center. Its precise convergence rate uniformly over all centers are derived and the convergence rate in mean square is described. These results present same optimality as that of the density estimator on a know orientation. At last, we give a example of estimator (θ)n for θ0.%设x为p维随机向量,对于未知的投影方向θ0(‖θ0‖=1),本文利用θ0的估计与核密度估计相结合的方法给出了θ0rX的密度(方向密度)的核型密度估计,获得了此估计的逐点渐近正态性,逐点精确强收敛率、一致精确强收敛率以及均方误差收敛率,所得结果与最优性与已知方向上的核密度估计完全一致,作为例子,对θ0为X协方差阵的最大特征值所对应的特征方向,我们给出了θ0的满足条件的估计极其方向密度估计.