We study the problem of nonparametric regression when the regressor is endogenous, which is an important nonparametric instrumental variables (NPIV) regression in econometrics and a difficult ill-posed inverse problem with unknown operator in statistics. We first establish a general upper bound...

We study the problem of nonparametric regression when the regressor is endogenous, which is an important nonparametric instrumental variables (NPIV) regression in econometrics and a difficult ill-posed inverse problem with unknown operator in statistics. We first establish a general upper bound...

Consider the linear model E[y|x] = x′β where one is interested in learning about β given data on y and x and when y is interval measured, i.e., we observe ([y0,y1],x) such that P(y ∈ [y0,y1]) = 1. Moment inequality procedures use the implication E[y0|x] ≤ x′β ≤ E[y1|x]. As compared...

We show that spline and wavelet series regression estimators for weakly dependent regressors attain the optimal uniform (i.e. sup-norm) convergence rate (n= log n)..p=(2p+d) of Stone (1982), where d is the number of regressors and p is the smoothness of the regression function. The optimal rate...