Open Access
December, 1991 Ignorability and Coarse Data
Daniel F. Heitjan, Donald B. Rubin
Ann. Statist. 19(4): 2244-2253 (December, 1991). DOI: 10.1214/aos/1176348396


We present a general statistical model for data coarsening, which includes as special cases rounded, heaped, censored, partially categorized and missing data. Formally, with coarse data, observations are made not in the sample space of the random variable of interest, but rather in its power set. Grouping is a special case in which the degree of coarsening is known and nonstochastic. We establish simple conditions under which the possible stochastic nature of the coarsening mechanism can be ignored when drawing Bayesian and likelihood inferences and thus the data can be validly treated as grouped data. The conditions are that the data be coarsened at random, a generalization of the condition missing at random, and that the parameters of the data and the coarsening process be distinct. Applications of the general model and the ignorability condition are illustrated in a numerical example and described briefly in a variety of special cases.


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Daniel F. Heitjan. Donald B. Rubin. "Ignorability and Coarse Data." Ann. Statist. 19 (4) 2244 - 2253, December, 1991.


Published: December, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0745.62004
MathSciNet: MR1135174
Digital Object Identifier: 10.1214/aos/1176348396

Primary: 62F99
Secondary: 62A10 , 62A15

Keywords: Censord data , coarsened at random , grouped data , heaped data , interval-censored data , missing at random , missing data , rounded data

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 4 • December, 1991
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