We consider a random design model based on independent and identically distributed (iid) pairs of observations (Xi, Yi), where the regression function m(x) is given by m(x) = E(Yi|Xi = x) with one independent variable. In a nonparametric setting the aim is to produce a reasonable approximation...

We consider a random design model based on independent and identically distributed pairs of observations (Xi, Yi), where the regression function m(x) is given by m(x) = E(Yi|Xi = x) with one independent variable. In a nonparametric setting the aim is to produce a reasonable approximation to the...

We propose an instrumental variables method for inference in high-dimensional structural equations with endogenous regressors. The number of regressors K can be much larger than the sample size. A key ingredient is sparsity, i.e., the vector of coefficients has many zeros, or approximate...