未知方向密度估计的收敛率

设Ｘ为ｐ维随机向量，对于未知的投影方向θｏ（‖θｏ‖＝１），本文利用θｏ的估计与核密度估计相结合的方法给出了θ＾Ｔ０Ｘ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θｏ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θｏ的满足条件的估计极其方向密度估计。

Rate of Convergence of the Density Estimator on an Unknown Orientation

Motivated by recent work on exploratory projection pursuit, we give the kernel estimator of density on an unknown projection orientation by combining the estimator of with classical kernel estimation and obtain its asymptotically normality at a fixed center. Its precise convergence rate uniformly over all canters 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. for .