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Abstract:
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In this paper, we study the problem of variance estimation for a domain total when auxiliary value imputation, sometimes called cold-deck or substitution imputation, has been used to fill in missing data. We consider two approaches to inference, which lead to different variance estimators. In the first approach, the validity of an imputation model is required. Our proposed variance estimator is nevertheless robust to misspecification of the second moment of the model. Under this approach, we show the somewhat counter-intuitive result that the total variance of the imputed estimator can be smaller than the sampling variance of the complete-data estimator. We also show that the naïve variance estimator (i.e. the variance estimator obtained by treating the imputed values as observed values) is asymptotically a valid estimator of the total variance when the sampling fraction is negligible.
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