The Annals of Statistics

Missing at random, likelihood ignorability and model completeness

Guobing Lu and John B. Copas

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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.

Article information

Ann. Statist. Volume 32, Number 2 (2004), 754-765.

First available in Project Euclid: 28 April 2004

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Zentralblatt MATH identifier

Primary: 62B99: None of the above, but in this section 62F10: Point estimation 62N01: Censored data models

Incomplete data missing at random coarsening at random ignorability complete distribution family


Lu, Guobing; Copas, John B. Missing at random, likelihood ignorability and model completeness. Ann. Statist. 32 (2004), no. 2, 754--765. doi:10.1214/009053604000000166.

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