  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.
