Density Level Sets: Asymptotics, Inference, and Visualization

• 成果类型: Article
• 署名作者: Chen, Yen-Chi; Genovese, Christopher R.; Wasserman, Larry
• 署名单位: University of Washington; University of Washington Seattle; Carnegie Mellon University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2016.1228536
• 发表日期: 2017
• 页码: 1684-1696
• 关键词: nonparametric-estimation; cluster tree; scale-space; mean shift; confidence; Consistency; uniform

摘要

We study the plug-in estimator for density level sets under Hausdorff loss. We derive asymptotic theory for this estimator, and based on this theory, we develop two bootstrap confidence regions for level sets. We introduce a new technique for visualizing density level sets, even in multidimensions, which is easy to interpret and efficient to compute. Supplementary materials for this article are available online.