Possibility Measures for Valid Statistical Inference Based on Censored Data
Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:49-58, 2019.
Inferential challenges that arise when data are corrupted by censoring have been extensively studied under the classical frameworks. In this paper, we provide an alternative approach based on a generalized inferential model whose output is a data-dependent possibility distribution. This construction is driven by an association between the censored data, parameter of interest, and unobserved auxiliary variable that takes the form of a relative likelihood. The possibility distribution then emerges from the introduction of a nested random set designed to predict that unobserved auxiliary variable and is calibrated to achieve certain frequentist guarantees. The performance of the proposed method is investigated using real and simulated data.