On the Existence of Strongly Consistent Indirect Estimators When the Binding Function Is Compact Valued

We provide sufficient conditions for the definition and the existence of strongly consistent indirect estimators when the binding function is a compact valued correspondence. We use conditions that concern the asymptotic behavior of the epigraphs of the criteria involved, a relevant notion of continuity for the binding correspondence as well as an indirect identification condition that restricts the behavior of the aforementioned correspondence. These are generalizations of the analogous results in the relevant literature and hence permit a broader scope of statistical models. We examine simple examples involving Levy and ergodic conditionally heteroskedastic processes.