This paper studies the estimation of a nonparametric function ' from the inverse problem r = T' given estimates of the function r and of the linear transform T. The rate of convergence of the estimator is derived under two assumptions expressed in a Hilbert scale. The approach provides a unified...

We consider the semiparametric regression Xtβ+φ(Z) where β and φ(·) are unknown slope coefficient vector 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...

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 consider the nonparametric regression model with an additive error that is correlated with the explanatory variables. We suppose the existence of instrumental variables that are considered in this model for the identification and the estimation of the regression function. The nonparametric...