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 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...

We consider the problem of testing hypotheses regarding the covariance matrix of multivariate normal data, if the sample size s and dimension n satisfy lim [n,s→∞] n/s = y. Recently, several tests have been proposed in the case, where the sample size and dimension are of the same order, that...