方向数据密度函数的最近邻估计

Nearest Neighbor Estimator for Density Function of Directional Data

设 Ｘ为取值于 ｄ＋ １维空间中单位球面上的单位随机向量，具有概率密度函数 ｆ（ｘ）本文讨论密度函数ｆ（ｘ）的估计问题，给出了基于方向数据的最近邻估计，并建立这种最近邻估计的逐点强，弱相合性，一致强相合性及渐近正态性。

Let X be a unit random vector, taking value on the surface of a unit sphere in d + 1 dimensional Euclidean space, with pdf f(x) which needs to be estimated. In this paper, we intruduce a kind of nearest neighbor estimator of f(x) based on directional data and establish pointwise, strong and weak consistency, uniformly strong consistency and asymptotic normality for this estimator. The results obtained in this paper are fundamentally similar to those based on Euclidean data in Rd.