Optimal Pseudolikelihood Estimation in Multivariate Missing Data with Nonignorable Nonresponse

• Activity Number: 6 - Recent Advance of Nonparametric and Semiparametric Techniques with Complex Data Structure
• Type: Invited
• Date/Time: Sunday, July 29, 2018 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jiwei Zhao and Yanyuan Ma*
• Companies: State University of New York At Buffalo and Penn State University
• Keywords: missing nonignorable; effiiency; pseudolikelihood

Abstract

Tang, Little and Raghunathan (2003, Biometrika) considered a regression model with missing response, where the missing mechanism depends on the underlying value of the response variable and hence is nonignorable. They proposed three different pseudolikelihood estimators, based on three different treatments to the probability distribution of the completely observed covariates. The first assumes the distribution of the covariate to be known, the second estimates the distribution parametrically, and the third nonparametrically estimates the distribution through its empirical distribution. While it is not hard to show that the second estimator is more efficient than the first one, due to the complexity, Tang et al only conjectured that the third estimator is more efficient than the first two. In this paper, we investigate the asymptotic behavior of the third estimator by providing a closed-form representation of its asymptotic variance. We then prove that the third estimator is indeed more efficient than the other two. We show that our result can be straightforwardly applied to missingness mechanisms that are more general than that in Tang et al.