Efficiency Bounds For Semiparametric Estimation Of Inverse Conditional-Density-Weighted Functions
Consider the unconditional moment restriction E[ m ( y , υ , w ; π 0 )/ f null ( 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 null -consistent regular estimators of null 0 can have is calculated when f null (·) is only known to be a bounded, continuous, nonzero conditional density function. Our results show that “plug-in” kernel-based estimators of null 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.
Volume (Year): 25 (2009)
Issue (Month): 03 (June)
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