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Abstract:
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A great deal of efforts has been devoted to the inference of additive model in the last decade. Among the many existing procedures, the kernel type are too costly to implement for large number of variables or for large sample sizes, while the spline type provides no asymptotic distribution or any measure of uniform accuracy. We propose a synthetic estimator of the component function in an additive regression model, using a one step backfitting, with spline estimators in the first stage and kernel estimators for the second stage. It is established that under very weak conditions, the proposed estimator's pointwise distribution is asymptotically equivalent to an ordinary univariate Nadaraya-Watson estimator, hence the dimension is effectively reduced to one at any point. This dimension reduction holds uniformly over an interval under stronger assumptions of normal errors.
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