Das Kunal, Yu Shan, Wang Guannan, Wang Li
Department of Statistics, Iowa State University, Ames, IA, 50011, USA.
Department of Statistics, University of Virginia, Charlottesville, VA, 22901, USA.
J Nonparametr Stat. 2025 Apr 28. doi: 10.1080/10485252.2025.2497541.
Accurately estimating data density is crucial for making informed decisions and modeling in various fields. This paper presents a novel nonparametric density estimation procedure that utilizes bivariate penalized spline smoothing over triangulation for data scattered over irregular spatial domains. Our likelihood-based approach incorporates a regularization term addressing the roughness of the logarithm of density using a second-order differential operator. We establish the asymptotic convergence rate of the proposed density estimator in terms of the and norms under mild natural conditions, providing a solid theoretical foundation. The proposed method demonstrates superior efficiency and flexibility with enhanced smoothness and continuity across the domain compared to existing techniques. We validate our approach through comprehensive simulation studies and apply it to real-world motor vehicle theft data from Portland, Oregon, illustrating its practical advantages in data analysis on spatial domains.
准确估计数据密度对于在各个领域做出明智决策和进行建模至关重要。本文提出了一种新颖的非参数密度估计方法，该方法利用三角剖分上的双变量惩罚样条平滑处理来处理散布在不规则空间域中的数据。我们基于似然的方法纳入了一个正则化项，使用二阶微分算子来处理密度对数的粗糙度。在温和的自然条件下，我们根据 和 范数建立了所提出密度估计器的渐近收敛速度，提供了坚实的理论基础。与现有技术相比，所提出的方法在整个域上具有更高的平滑度和连续性，展示出卓越的效率和灵活性。我们通过全面的模拟研究验证了我们的方法，并将其应用于来自俄勒冈州波特兰市的实际机动车盗窃数据，说明了其在空间域数据分析中的实际优势。
