1. the presence of heteroskedasticity of unknown form, and showed that his estimator reached the semiparametric e� ciency bound. Ai and Chen (2003) propose semiparametrically e� cient sieve estimators for a class of semiparametric models described by conditional moment restrictions. For an introduction to and general results on copulas;Robinson;Luenberger (1969) and Kantorovich and Akilov,1982
2. Chamberlain (1987, 1992) derive e� ciency bounds for conditional moment restrictions and semiparametric regressions. Manski (1984) develop e� ciency bounds and adaptive estimators for nonlinear regression models under independence assumption; see Drost and Klaassen (1997) for similar results in the case of heteroskedastic time series models. We have not discussed the practical implementation of semiparametric estimators. We refer to Ichimura and Todd (2007) for an overview. Cattaneo et al (2009) discuss in detail bandwidth selection for average derivative estimators, while H�rdle et al (1993) propose a speci?c method for the single-index models. We have throughout assumed that data was i.i.d. Most of the asymptotic results for the proposed estimators go through for stationary and mixing sequences;Linton Chen;Our asymptotic results for semiparametric two-step estimators are similar to those found in, amongst others,1987
3. E� cient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions;C Ai;Econometrica,2003