In this paper, we study a nonparametric regression model including a periodic component, a smooth trend function, and a stochastic error term. We propose a procedure to estimate the unknown period and the function values of the periodic component as well as the nonparametric trend function. The...

We establish the consistency and asymptotic normality for a class of estimators that are linear combinations of a set of √n– consistent estimators whose cardinality increases with sample size. A special case of our framework corresponds to the conditional moment restriction and the implied...