We consider the semiparametric regression X t +(Z) where and (r and function, and where the variables (X, Z) are endogeneous. We propose necessary and sufficient conditions for the identification of the parameters in the presence of instrumental variables. We also focus on the estimation of . An...

The nonparametric estimation of a regression function from conditional moment restrictions involving instrumental variables is considered. The rate of convergence of penalized estimators is studied in the case where the regression function is not identified from the conditional moment...

This paper studies the estimation of a nonparametric function <italic>ϕ</italic> from the inverse problem <italic>r</italic> = <italic>Tϕ</italic> given estimates of the function <italic>r</italic> and of the linear transform <italic>T</italic>. We show that rates of convergence of the estimator are driven by two types of assumptions expressed in a single Hilbert scale. The...

We estimate the distribution of a real-valued random variable from contaminated observations. The additive error is supposed to be normally distributed, but with an unknown variance. The distribution is identifiable from the observations if we restrict the class of considered distributions by a...