Local or global smoothing? A bandwidth selector for dependent data

The selection of the smoothing parameter represents a crucial step in local polynomial regression, due to the implications on the consistency of the non-parametric estimator and to the difficulties in the implementation of the selection procedure. In order to capture the complexity of the unknown regression curve, a local variable bandwidth may be used, but this may increase the variability of the estimates and the computational costs. This paper focuses on the problem of estimating the smoothing parameter adaptively on the support of the function, after evaluating the effective gain in using a local bandwidth rather than a global one.