  In this paper we introduce new estimators of the coefficient functions in the
varying coefficient regression model. The proposed estimators are obtained by
projecting the vector of the full-dimensional kernel-weighted local polynomial
estimators of the coefficient functions onto a Hilbert space with a suitable
norm. We provide a backfitting algorithm to compute the estimators. We show
that the algorithm converges at a geometric rate under weak conditions. We
derive the asymptotic distributions of the estimators and show that the
estimators have the oracle properties. This is done for the general order of
local polynomial fitting and for the estimation of the derivatives of the
coefficient functions, as well as the coefficient functions themselves. The
estimators turn out to have several theoretical and numerical advantages over
the marginal integration estimators studied by Yang, Park, Xue and H\"{a}rdle
[J. Amer. Statist. Assoc. 101 (2006) 1212--1227].
