ASYMPTOTIC THEORY FOR DENSITY RIDGES

• 成果类型: Article
• 署名作者: Chen, Yen-Chi; Genovese, Christopher R.; Wasserman, Larry
• 署名单位: Carnegie Mellon University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1329
• 发表日期: 2015
• 页码: 1896-1928
• 关键词: curve reconstruction; uniform consistency; approximation

摘要

The large sample theory of estimators for density modes is well understood. In this paper we consider density ridges, which are a higher-dimensional extension of modes. Modes correspond to zero-dimensional, local high-density regions in point clouds. Density ridges correspond to s-dimensional, local high-density regions in point clouds. We establish three main results. First we show that under appropriate regularity conditions, the local variation of the estimated ridge can be approximated by an empirical process. Second, we show that the distribution of the estimated ridge converges to a Gaussian process. Third, we establish that the bootstrap leads to valid confidence sets for density ridges.