Abstract: Nonresponse is very common in survey sampling. Nonignorable nonresponse, a response mechanism in which the response probability of a survey variable depends directly on the value of regardless of whether is observed or not, is the most difficult type of nonresponse to handle. The population mean estimators ignoring the nonrespondents typically have heavy biases. This paper studies an empirical likelihood-based estimation method, with samples under nonignorable nonresponse, when an observed auxiliary categorical variable is available. The likelihood is semiparametric: we assume a parametric model on the response mechanism and the conditional probability of given , and a nonparametric model on the distribution of . When the number of categories is not small, a pseudo empirical likelihood method is applied to reduce the computational intensity. Asymptotic distributions of the proposed population mean estimators are derived. For variance estimation, we consider a bootstrap procedure and its consistency is established. Some simulation results are provided to assess the finite sample performance of the proposed estimators.
Key words and phrases: Empirical likelihood, nonignorable nonresponse, pseudo likelihood, sample survey, semiparametric likelihood, stratified samples.