Nonparametric estimation of response probabilities in sampling theory

We deal with the nonresponse problem by drawing on the model of selection in phases that was proposed by Särndal and Swenson (1987). To estimate response probabilities, we use the nonparametric approach first advanced by Giommi (1987). We define estimators according to the nonparametric estimation (NPE) model, and we study their general properties empirically. Inference is based on the concept of quasi-randomization (Oh and Scheuren 1983). The emphasis is on estimating the variance and constructing confidence intervals. We find, by way of a Monte Carlo study, that it is possible to improve the quality of the estimators considered by using a variant of the NPE approach. The latter also serves to confirm the performance of regression estimators in terms of variance estimation.