Sample-constrained partial identification with application to selection bias

Understand

Many partial identification problems can be characterized by the optimal value of a function over a set where both the function and set need to be estimated by empirical data.

• Despite some progress for convex problems, statistical inference in this general setting remains to be developed.
• To address this, we derive an asymptotically valid confidence interval for the optimal value through an appropriate relaxation of the estimated set.
• We then apply this general result to the problem of selection bias in population-based cohort studies.