Estimating equations inference with missing data

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

52 Scopus Citations
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Detail(s)

Original languageEnglish
Pages (from-to)1187-1199
Journal / PublicationJournal of the American Statistical Association
Volume103
Issue number483
Publication statusPublished - Sep 2008

Abstract

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 universally 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 when data are missing at random. The investigation is motivated by the observation that direct imputation of missing data in 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 reformulation 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. © 2008 American Statistical Association.

Research Area(s)

  • Empirical likelihood, Estimating equations, Generalized method of moments, Kernel regression, Missing at random, Reduced dimension