TY - JOUR
T1 - Estimating equations inference with missing data
AU - Zhou, Yong
AU - Wan, Alan T. K.
AU - Wang, Xiaojing
PY - 2008/9
Y1 - 2008/9
N2 - 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.
AB - 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.
KW - Empirical likelihood
KW - Estimating equations
KW - Generalized method of moments
KW - Kernel regression
KW - Missing at random
KW - Reduced dimension
UR - http://www.scopus.com/inward/record.url?scp=54949085047&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-54949085047&origin=recordpage
U2 - 10.1198/016214508000000535
DO - 10.1198/016214508000000535
M3 - RGC 21 - Publication in refereed journal
SN - 0162-1459
VL - 103
SP - 1187
EP - 1199
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 483
ER -