AN ALGORITHMIC AND A GEOMETRIC CHARACTERIZATION OF COARSENING AT RANDOM

• 成果类型: Article
• 署名作者: Gill, Richard D.; Grunwald, Peter D.
• 署名单位: Leiden University - Excl LUMC; Leiden University; Centrum Wiskunde & Informatica (CWI)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS532
• 发表日期: 2008
• 页码: 2409-2422
• 关键词: ignorability

摘要

We show that the class of conditional distributions satisfying the coarsening at random (CAR) property for discrete data has a simple and robust algorithmic description based oil randomized uniform multicovers: combinatorial objects generalizing the notion of partition of a set. However, the complexity of a given CAR mechanism can be large: the maximal height of the needed multicovers can be exponential in the number of points, in the sample space. The results stein from a geometric interpretation of the set of CAR distributions as a convex polytope and a characterization of its extreme points. The hierarchy of CAR models defined in this way could be useful in parsimonious statistical modeling of CAR mechanisms, though the results also raise doubts in applied work as to the meaningfulness of the CAR assumption in its full generality.