Shape-constrained partial identification of a population mean under unknown probabilities of sample selection

Abstract

Summary Estimating a population mean from a sample obtained with unknown selection probabilities is important in the biomedical and social sciences. Using a ratio estimator, Aronow & Lee (2013) proposed a method for partial identification of the mean by allowing the unknown selection probabilities to vary arbitrarily between two fixed values. In this paper, we show how to use auxiliary shape constraints on the population outcome distribution, such as symmetry or log-concavity, to obtain tighter bounds on the population mean. We use this method to estimate the performance of Aymara students, an ethnic minority in the north of Chile, in a national educational standardized test. We implement this method in the R package scbounds.