Location-scale depth

• 成果类型: Article
• 署名作者: Mizera, I; Müller, CH
• 署名单位: University of Alberta; Carl von Ossietzky Universitat Oldenburg
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214504000001312
• 发表日期: 2004
• 页码: 949-966
• 关键词: half-space depth; regression; contours; estimators; CONVERGENCE; asymptotics; statistics; notion

摘要

This article introduces a halfspace depth in the location-scale model that is along the lines of the general theory given by Mizera, based on the idea of Rousseeuw and Hubert, and is complemented by a new likelihood-based principle for designing criterial functions. The most tractable version of the proposed depth-the Student depth-turns Out to be nothing but the bivariate halfspace depth interpreted in the Poincare plane model of the Lobachevski geometry. This fact implies many fortuitous theoretical and computational properties, in particular equivariance with respect to the Mobius group and favorable time complexities of algorithms. It also opens a way to introduce some other depth notions in the location-scale context, for instance. location-scale simplicial depth. A maximum depth estimator of location and scale-the Student median-is introduced. Possible applications of the proposed concepts are investigated on data examples.