Estimating Equations Inference With Missing Data

Yong Zhou

doi:10.1198/016214508000000535

Estimating Equations Inference With Missing Data

2012-01-01

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DOI：10.1198/016214508000000535

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There is a large and growing body of literature on estimating equation (EE) as an estimation approach. One basic property of EE that has been universely adopted in practice is that of unbiasedness, and there are deep conceptual reasons why unbiasedness is a desirable EE characteristic. This article deals with inference from EEs generally leads to EEs that are biased and thus, violates a basic assumption of the EE approach. The main contribution of this article is that it goes beyond existing imputation methods and proposes a procedure whereby one mitigates the effects of missing data through a reformation of EEs imputed through a kernel regression method. These (modified) EEs then constitute a basis for inference by the generalized method of moments (GMM) and empirical likelihood (EL). Asymptotic properties of the GMM and EL estimators of the unknown parameters are derived and analyzed. Unlike most of the literature, which deals with missingness in either covariate values or response data, our method allows for missingness in both sets of variables. Another important strength of our approach is that it allows auxiliary information to be handled successfully. We illustrate the method using a well-known wormy-fruits dataset and data from a study on Duchenne muscular dystrophy detection and compare our results with several existing methods via a simulation study.

Keywords:

Empirical likelihood

Estimating equations

Generalized method of moments

Kernel regression

Missing at random

Reduced dimension

Estimating Equations Inference With Missing Data

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