Parametrically guided non-parametric regression

We present a new approach to regression function estimation in which a nonparametric regression estimator is guided by a parametric pilot estimate with the aim of reducing the bias. New classes of parametrically guided kernel weighted Local polynomial estimators are introduced and formulae for asymptotic expectation and variance, hence approximated mean squared error and mean integrated squared error, are derived. It is shown that the new classes of estimators have the very same large sample variance as the estimators in the standard non-parametric setting, while there is substantial room for reducing the bias if the chosen parametric pilot function belongs to a wide neighbourhood around the true regression line. Bias reduction Is discussed in light of examples and simulations.