Estimation with survey data under nonignorable nonresponse or informative sampling

Nonresponse is a very common phenomenon in survey sampling, Nonignorable nonresponse-that is, a response mechanism that depends on the values of the variable having nonresponse-is the most difficult type of nonresponse to handle. This article studies a likelihood-based estimation method for data with nonignorable nonresponse. The likelihood is semiparametric in the sense that it consists of a parametric component for the response mechanism (such as a logistic model) and a nonparametric component for the distribution of the variable of interest and the covariates. We show how auxiliary information can be augmented to improve the efficiency of estimators. Asymptotic distributions for the resulting parameter estimates are derived. A simulation study shows that the proposed method gives promising results. The method can also be applied to problems with two-phase sampling in which the second-phase sampling is informative.