Kernel Density Estimation with Spherical Data
研究了用于球面数据的两类核密度估计器，比较了它们的渐近性质，发现第二类中的某些估计器在平方误差或KL散度损失下优于第一类所有估计器，并给出了偏差、方差和损失的显式公式与大样本性质。
We study two natural classes of kernel density estimators for use with spherical data. Members of both classes have already been used in practice. The classes have an element in common, but for the most part they are disjoint. However, all members of the first class are asymptotically equivalent to one another, and to a single element of the second class. In this sense the second class ‘contains’ the first. It includes some estimators which out-perform all those in the first class, if loss is measured in either squared-error or Kullback—Leibler senses. Explicit formulae are given for bias, variance and loss, and large-sample properties of these quantities are described. Numerical illustrations are presented.