EFFICIENCY BOUNDS FOR SEMIPARAMETRIC ESTIMATION OF INVERSE CONDITIONAL-DENSITY-WEIGHTED FUNCTIONS
研究了在条件密度未知时，基于无条件矩限制的逆条件密度加权函数估计量的最小渐近方差，并证明Lewbel提出的核估计量是半参数有效的。
Consider the unconditional moment restriction E[ m ( y , υ , w ; π 0 )/ f V | w ( υ | w ) − s ( w ; π 0 )] = 0, where m (·) and s (·) are known vector-valued functions of data ( y ┬ , υ , w ┬ ) ┬ . The smallest asymptotic variance that $\root \of n $ -consistent regular estimators of π 0 can have is calculated when f V | w (·) is only known to be a bounded, continuous, nonzero conditional density function. Our results show that “plug-in” kernel-based estimators of π 0 constructed from this type of moment restriction, such as Lewbel (1998, Econometrica 66, 105–121) and Lewbel (2007, Journal of Econometrics 141, 777–806), are semiparametric efficient.