Publication Date: September 1997
We derive the asymptotic distribution of a new backﬁtting procedure for estimating the closest additive approximation to a nonparametric regression function. The procedure employs a recent projection interpretation of popular kernel estimators provided by Mammen et al. (1997), and the asymptotic theory of our estimators is derived using the theory of additive projections reviewed in Bickel et al. (1995). Our procedure achieves the same bias and variance as the oracle estimator based on knowing the other components, and in this sense improves on the method analyzed in Opsomer and Ruppert (1997). We provide ‘high level’ conditions independent of the sampling scheme. We then verify that these conditions are satisﬁed in a time series autoregression under weak conditions.
Published in The Annals of Statistics (October 1999), 27(5): 1443-1490 [JSTOR]