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ABSTRACT
We consider multivariate small area estimation under nonignorable, not missing at random (NMAR) nonresponse. We assume a response model that accounts for the different patterns of the observed outcomes, (which values are observed and which ones are missing), and estimate the response probabilities by application of the Missing Information Principle (MIP). By this principle, we first derive the likelihood score equations for the case where the missing outcomes are actually observed, and then integrate out the unobserved outcomes from the score equations with respect to the distribution holding for the missing data. The latter distribution is defined by the distribution fitted to the observed data for the respondents and the response model. The integrated score equations are then solved with respect to the unknown parameters indexing the response model. Once the response probabilities have been estimated, we impute the missing outcomes from their appropriate distribution, yielding a complete data set with no missing values, which is used for predicting the target area means. A parametric bootstrap procedure is developed for assessing the mean squared errors (MSE) of the resulting predictors. We illustrate the approach by a small simulation study.
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No potential conflict of interest was reported by the authors.
Notes
* The opinions expressed in this paper are of the authors and do not necessarily represent the policies of the U.S. Bureau of Labor Statistics and the Israel Central Bureau of Statistics.
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Notes on contributors
Danny Pfeffermann
Danny Pfeffermann is currently the National Statistician and General Director of the Central Bureau of Statistics of Israel. His main research areas are analytic inference from complex sample surveys and in particular, informative samples with non-ignorable nonresponse, small area estimation, seasonal adjustment and trend estimation and recently, accounting for mode effects and proxy surveys.
Michael Sverchkov
Michael Sverchkov is a Research Mathematical Statistician at the US Bureau of Labor Statistics. His main research areas are analytic inference from complex sample surveys and in particular, informative samples with non-ignorable nonresponse, small area estimation, seasonal adjustment.