A note on combining parametric and non-parametric regression

Abstract

A combination of a parametric estimate and a nonparametric estimate of a model for a regression function is considered. The optimal linear combination is estimated from the data by the least squares estimate of the combining coefficient. The estimate so obtained is compared with the one proposed by Wooldridge (1992) and Burman and Chaud-huri,the latter being based on Stein (1956). A test procedure for deciding about the parametric specification is also studied.