This paper studies the problem of specification testing in partially identified models defined by moment (in)equalities. This problem has not been directly addressed in the literature, although several papers have suggested a test based on checking whether confidence sets for the parameters of...

This paper develops methods of inference for nonparametric and semiparametric parameters defined by conditional moment inequalities and/or equalities. The parameters need not be identified. Confidence sets and tests are introduced. The correct uniform asymptotic size of these procedures is...

This paper presents sieve inferences on possibly irregular (i.e., slower than root-n estimable) functionals of semi-nonparametric models with i.i.d. data. We provide a simple consistent variance estimator of the plug-in sieve M estimator of a possibly irregular functional, and the asymptotic...

This paper establishes the asymptotic normality of plug-in sieve M estimators of possibly irregular functionals of semi-nonparametric time series models. We show that, even when the sieve score process is not a martingale difference sequence, the asymptotic variance in the case of irregular...