We consider models defined by conditional moment restrictions under semi-strong identification. Identification strength is directly defined through the conditional mo- ments that flatten as the sample size increases. The framework allows for different iden- tification strengths across...

A generalization of the Cauchy-Schwarz inequality for expectations of matrices is proved.

We develop a novel approach to build checks of parametric regression models when many regressors are present, based on a class of rich enough semiparametric alternatives, namely single-index models. We propose an omnibus test based on the kernel method that performs against a sequence of...

We propose a new estimation method for models defined by conditional moment restrictions,that minimizes a distance criterion based on kernel smoothing. Whether the bandwidth parameter is fixed or decreases to zero with the sample size, our approach defines a whole class of estimators. We develop...