In an increasing number of empirical studies, the dimensionality measured e.g. as the size of the parameter space of interest, can be very large. Two instances of large dimensional models are the linear regression with a large number of covariates and the estimation of a regression function with...

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...

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 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...