  We discuss local linear smooth backfitting for additive non-parametric
models. This procedure is well known for achieving optimal convergence rates
under appropriate smoothness conditions. In particular, it allows for the
estimation of each component of an additive model with the same asymptotic
accuracy as if the other components were known. The asymptotic discussion of
local linear smooth backfitting is rather complex because typically an
overwhelming notation is required for a detailed discussion. In this paper we
interpret the local linear smooth backfitting estimator as a projection of the
data onto a linear space with a suitably chosen semi-norm. This approach
simplifies both the mathematical discussion as well as the intuitive
understanding of properties of this version of smooth backfitting.
