Efficiency bounds for semiparametric estimation of inverse conditional-density-weighted functions | David Jacho-Chavez

# Efficiency bounds for semiparametric estimation of inverse conditional-density-weighted functions

### Abstract

Consider the unconditional moment restriction ${E[m(y,v,w;\pi_{0})/f_{V|w} (v|w) s(w;\pi_{0})] = 0}$, where ${m(\cdot)}$ and ${s(\cdot)}$ are known vector-valued functions of data ${(y^\prime,v,w^\prime)^\prime}$. The smallest asymptotic variance that √n-consistent regular estimators of 0 can have is calculated when ${f_{V|w}(\cdot)}$ is only known to be a bounded, continuous, nonzero conditional density function. Our results show that plug-in kernel-based estimators of ${\pi_{0}}$ constructed from this type of moment restriction, such as Lewbel (1998, Econometrica 66, 105121) and Lewbel (2007, Journal of Econometrics 141, 777806), are semiparametric efficient.

Publication
Econometric Theory, (25), 3, pp. 847-855