Missing at random, likelihood ignorability and model completeness. (English) Zbl 1048.62007

Summary: This paper provides further insight into the key concept of missing at random (MAR) in incomplete data analysis. Following the usual selection modelling approach we envisage two models with separable parameters: a model for the response of interest and a model for the missing data mechanism (MDM). If the response model is given by a complete density family, then frequentist inference from the likelihood function ignoring the MDM is valid if and only if the MDM is MAR. This necessary and sufficient condition also holds more generally for models for coarse data, such as censoring. Examples are given to show the necessity of the completeness of the underlying model for this equivalence to hold.


62A01 Foundations and philosophical topics in statistics
62B99 Sufficiency and information
62F10 Point estimation
62N01 Censored data models
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