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

Omar, Aziz und Augustin, Thomas (2019): Estimation of classification probabilities in small domains accounting for nonresponse relying on imprecise probability. In: International Journal of Approximate Reasoning, Bd. 115: S. 134-143

Abstract

In this paper, we propose two generalized Bayesian imprecise probability approaches for estimation of proportions under potentially nonignorable nonresponse using data from small domains. Our approaches produce reliable inference, refraining from strong assumptions on the response process that are typically not testable. Hence, our estimates avoid the possibly severe bias arising from fallaciously imposing such assumptions. Specifically, we generalize the imprecise Beta model to the small area estimation setting, first treating the missing values in a radically cautious way and then deriving a method that allows incorporating powerfully weak knowledge on the missingness process. Additionally, we extend the empirical Bayes small area estimation approach applied by Stasny [27] through considering a set of priors arising from neighborhood of maximum likelihood estimates of the hyperparameters. As an illustration, we reanalyze data from the American National Crime Survey to estimate the probability of victimization in domains formed by cross-classification of certain characteristics. (C) 2019 Elsevier Inc. All rights reserved.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Statistik ; Psychologie und Pädagogik > Department Psychologie
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik ; 100 Philosophie und Psychologie > 150 Psychologie
• ISSN: 0888-613X
• Sprache: Englisch