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Abstract

We derive the asymptotic distribution of a new backfitting procedure for estimating the closest additive approximation to a nonparametric regressionfunction. The procedure employs a recent projection interpretation ofpopular kernel estimators provided by Mammen et al. (1997), and theasymptotic theory of our estimators is derived using the theory of additiveprojections reviewed in Bickel et al. (1995). Our procedure achieves thesame bias and variance as the oracle estimator based on knowing the othercomponents, and in this sense improves on the method analyzed in Opsomer andRuppert (1997). We provide 'high level' conditions independent of thesampling scheme. We then verify that these conditions are satisfied in atime series autoregression under weak conditions.