The silhouette, concentration functions and ML-density estimation under order restrictions

• 成果类型: Article
• 署名作者: Polonik, W
• 署名单位: Ruprecht Karls University Heidelberg
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 1857-1877
• 关键词: generalized quantile processes; dimensions; contour

摘要

Based on empirical Levy-type concentration functions, a new graphical representation of the ML-density estimator under order restrictions is given. This representation generalizes the well-known representation of the Grenander estimator of a monotone density as the slope of the least concave majorant of the empirical distribution function to higher dimensions and arbitrary order restrictions. From the given representation it follows that a density estimator called silhouette, which arises naturally out of the excess mass approach, is the ML-density estimator under order restrictions. This fact provides a new point of view to ML-density estimation from which one gains additional insight to this problem, as demonstrated in the present paper.