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October 2008 An algorithmic and a geometric characterization of coarsening at random
Richard D. Gill, Peter D. Grünwald
Ann. Statist. 36(5): 2409-2422 (October 2008). DOI: 10.1214/07-AOS532


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 on 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 stem 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.


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Richard D. Gill. Peter D. Grünwald. "An algorithmic and a geometric characterization of coarsening at random." Ann. Statist. 36 (5) 2409 - 2422, October 2008.


Published: October 2008
First available in Project Euclid: 13 October 2008

zbMATH: 1148.62005
MathSciNet: MR2458192
Digital Object Identifier: 10.1214/07-AOS532

Primary: 62A01
Secondary: 62N01

Keywords: Coarsening at random (CAR) , Fibonacci numbers , ignorability , uniform multicover

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 5 • October 2008
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