Nonparametric Density Estimation Over Complicated Domains
提出一种非参数方法，用于在形状复杂的空间区域上估计密度，结合似然和微分算子正则化，利用有限元技术高效计算，能处理复杂边界、凹洞和多峰各向异性信号，在模拟和波特兰犯罪数据中优于现有方法。
Abstract We propose a nonparametric method for density estimation over (possibly complicated) spatial domains. The method combines a likelihood approach with a regularization based on a differential operator. We demonstrate the good inferential properties of the method. Moreover, we develop an estimation procedure based on advanced numerical techniques, and in particular making use of finite elements. This ensures high computational efficiency and enables great flexibility. The proposed method efficiently deals with data scattered over regions having complicated shapes, featuring complex boundaries, sharp concavities or holes. Moreover, it captures very well complicated signals having multiple modes with different directions and intensities of anisotropy. We show the comparative advantages of the proposed approach over state of the art methods, in simulation studies and in an application to the study of criminality in the city of Portland, Oregon.