Additive regression models have turned out to be a useful
statistical tool in analyses of high-dimensional data sets. Recently, an
estimator of additive components has been introduced by Linton and Nielsen
which is based on marginal integration. The explicit definition of this
estimator makes possible a fast computation and allows an asymptotic
distribution theory. In this paper an asymptotic treatment of this estimate is
offered for several models. A modification of this procedure is introduced. We
consider weighted marginal integration for local linear fits and we show that
this estimate has the following advantages.
¶ (i) With an appropriate choice of the weight function, the additive
components can be efficiently estimated: An additive component can be estimated
with the same asymptotic bias and variance as if the other components were
known.
¶ (ii) Application of local linear fits reduces the design related
bias.