Sieve M Inference on Irregular Parameters

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 functionals, which implies that the sieve t statistic is asymptotically standard normal. We show that, even for hypothesis testing of irregular functionals, the sieve likelihood ratio statistic is asymptotically Chi-square distributed. These results are useful in inference on structural parameters that may have singular semiparametric e¢ ciency bounds. The proposed inference methods are investigated in a simulation study and an empirical example. JEL Classi…cation: C12, C14