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Abstract:
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Missing data is a common problem that impedes the task of making inference for population parameters of interest. A popular method for handling missing data is multiple imputation (Rubin 2004) where the inference accounts for uncertainity due to missing data. This inference comes from combining the point and variance estimates from imputed data sets via Rubin's traditional combining rules. A sufficient condition for these combining rules is that the point estimate be approximately (multivariate) normally distributed. This paper explores and provides rules for combining non-normal test-statistics, specifically, F- and Beta- distributed test-statistics, from imputed data to make inference for population parameters of interest. These combining rules have the advantage of being computationally convenient since they only involve combining 1-dimensional entities, while the traditional combining rules get computationally cumbersome when the dimension of the parameter of interest is large. This paper demonstrates, both theoretically and via simulations, that the proposed combining rules possess good statistical properties and computation efficiency.
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