IGNORABILITY AND COARSE DATA
IGNORABILITY AND COARSE DATA
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DOI：
10.1214/aos/1176348396
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发表时间：
1991-12-01
影响因子：
4.5
通讯作者：
RUBIN, DB
中科院分区：
文献类型：
--
作者：
HEITJAN, DF;RUBIN, DB
我们提出了一个用于数据粗化的一般统计模型，其中包括作为特殊情况的舍入、堆积、删节、部分分类和缺失数据。形式上，对于粗糙数据，不是在感兴趣的随机变量的样本空间中进行观察，而是在其幂集中进行观察。分组是一种特殊情况，其中粗化程度是已知的，并且是非随机的。我们建立了简单的条件，在此条件下，在进行贝叶斯和似然推理时可以忽略粗化机制可能的随机性质，从而可以有效地将数据作为分组数据处理。这些条件是随机粗化的数据、随机缺失条件的一般化、数据参数和粗化过程的参数不同。通过一个算例说明了一般模型和可忽略条件的应用，并简要说明了各种特殊情况下的应用。
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.