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

@article{Miratrix2017ShapeconstrainedPI, title={Shape-constrained partial identification of a population mean under unknown probabilities of sample selection}, author={Luke W. Miratrix and Stefan Wager and Jos{\'e} R. Zubizarreta}, journal={arXiv: Statistics Theory}, year={2017} }

A prevailing challenge in the biomedical and social sciences is to estimate a population mean from a sample obtained with unknown selection probabilities. Using a well-known ratio estimator, Aronow and Lee (2013) proposed a method for partial identification of the mean by allowing the unknown selection probabilities to vary arbitrarily between two fixed extreme values. In this paper, we show how to leverage auxiliary shape constraints on the population outcome distribution, such as symmetry or…

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