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We discuss local linear smooth backfitting for additive non-parametricmodels. This procedure is well known for achieving optimal convergence ratesunder appropriate smoothness conditions. In particular, it allows for theestimation of each component of an additive model with the same asymptoticaccuracy as if the other components were known. The asymptotic discussion oflocal linear smooth backfitting is rather complex because typically anoverwhelming notation is required for a detailed discussion. In this paper weinterpret the local linear smooth backfitting estimator as a projection of thedata onto a linear space with a suitably chosen semi-norm. This approachsimplifies both the mathematical discussion as well as the intuitiveunderstanding of properties of this version of smooth backfitting.

Local linear smoothing in additive models as data projection