Approximation to Locally Semiparametric Efficient Scores in Missing Data Problems through Likelihood Robustification

• Activity Number: 223
• Type: Topic Contributed
• Date/Time: Tuesday, August 9, 2005 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Hua Yun Chen*+
• Companies: University of Illinois, Chicago
• Keywords: Auxiliary variable ; Adjoint operator ; Convexity ; Numeric differentiation ; Projection

Abstract

In semiparametric models with missing data, the semiparametric efficient estimator often cannot be obtained without additional model assumption, even when the semiparametric efficient estimator has simple form when no missing data are involved. Robins et al. proposed to find the locally semiparametric efficient estimator as a compromise and showed the locally semiparametric efficient estimator has the doubly robust property when the missing data are missing at random in Rubin's sense. In practice, the approach proposed by Robins et al. to finding a locally semiparametric efficient estimator can be challenging to implement. We propose an approach to approximating locally semiparametric efficient scores through likelihood robustification. The proposed approach is flexible, relatively easy to implement, and can be applied to missing data with arbitrary missing patterns. The approximation estimator has the doubly robust property when missing data are MAR, and only requires correct specification of the missing data mechanism model for consistency when missing data are nonignorable. Estimation and inferences on the parameter are outlined.