Universiteit Utrecht

Department of Mathematics


Farewell to Coarsening at Random



Richard Gill (UU)
20 June 2006

“Coarsening at Random” (CAR) is the most general kind of missingness mechanism in statistics whose presence can be safely ignored in the statistical analysis - having observed that a random variable  X  took a value in a random set  B,  one can behave as if the partition  { BB-complement },  was set up in advance, independently of  X;  one simply observed whether  X  took a value in  B  or its complement.

Back in 1997, Gill, van der Laan and Robins posed a number of questions concerning the characterization of CAR. In particular, is there an algorithmic description of the class of CAR mechanisms? Are all CAR mechanisms honest, in the sense that the observer is told the whole truth needed to generate the outcome B, not just the truth? Recent work by Jaeger (2005, J.A.I.R.), and by Gill and Grunwald (arXiv.org: math.ST/0510276), has more or less closed this episode. In particular I'll show that all CAR mechanisms can be simulated by a generalized notion of partition which we call: uniform multicover. The algorithmic description follows from a simple geometric picture of the CAR mechanisms.


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Yuri Yakubovich