Estimation of classification probabilities in small domains accounting for nonresponse relying on imprecise probability

Abstract

Nonresponse treatment is usually carried out through imposing strong assumptions regarding the response process in order to achieve point identifiability of the parameters of interest. Problematically, such assumptions are usually not readily testable and fallaciously imposing them may lead to severely biased estimates. In this paper we develop generalized Bayesian imprecise probability methods for estimation of proportions under potentially nonignorable nonresponse using data from small domains. Namely, we generalize the imprecise Beta model to this setting, treating missing values in a cautious way. Additionally, we extend the empirical Bayes model introduced by Stasny (1991, JASA) by considering a set of priors arising, for instance, from neighborhoods of maximum likelihood estimates of the hyper parameters. We reanalyze data from the American National Crime Survey to estimate the probability of victimization in domains formed by cross-classification of certain characteristics.