A Profile Likelihood Approach to Semiparametric Estimation with Nonignorable Nonresponse

Abstract: Statistical inference with nonresponse is quite challenging, especially when the response mechanism is nonignorable. The existing methods often require correct model specifications for both outcome and response models. However, due to nonresponse, both models cannot be verified from data directly and model misspecification can lead to a seriously biased inference. To overcome this limitation, we develop a robust and efficient semiparametric method based on the profile likelihood. The proposed method uses the robust semiparametric response model, in which fully unspecified function of study variable is assumed. An efficient computation algorithm using fractional imputation is developed. A quasi-likelihood approach for testing ignorability is also developed. The consistency and asymptotic normality of the proposed method are established. The finite-sample performance is examined in the extensive simulation studies and an application to the Korean Labor and Income Panel Study dataset is also presented.