COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1160

The Existence and Asymptotic Properties of a
Backfitting Projection Algorithm under Weak Conditions

O. Linton, E. Mammen and J. Nielsen

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.