Parametric mixture models are commonly used in applied work, especially empirical economics, where these models are often employed to learn for example about the proportions of various types in a given population. This paper examines the inference question on the proportions (mixing probability)...

Consider the linear model E[y|x] = x′β where one is interested in learning about β given data on y and x and when y is interval measured, i.e., we observe ([y0,y1],x) such that P(y ∈ [y0,y1]) = 1. Moment inequality procedures use the implication E[y0|x] ≤ x′β ≤ E[y1|x]. As compared...