EMPIRICAL LIKELIHOOD ESTIMATION FOR SAMPLES WITH NONIGNORABLE NONRESPONSE

Nonresponse is my common in survey sampling Nonignorable nonresponse, a response mechanism in which the response probability of a survey variable Y depends directly oil the value of Y regardless of whether Y is observed or not, is the most difficult, type of nonresponse to handle The population mean estimators ignoring the nonrespondents typically have heavy biases. Ills paper studies all empirical likelihood-based estimation method, with samples under nonignorable nonresponse, when all observed auxiliary categorical variable Z is available The likelihood is semiparametric we assume a parametric model oil the response mechanism and the conditional probability of Y given Y, and a nonparametric model on the distribution of Y When the number of Z 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