Additive regression with parametric help

초록

Additive models have been studied as a way of overcoming theoretical and practical difficulties in estimating a multivariate nonparametric regression function. Several methods have been proposed that ensure the optimal univariate rate one can achieve in estimating univariate nonparametric functions. In this paper a new method is proposed which reduces the constant factor in the first-order approximation of the average squared error of the most successful existing method. The new estimator is based on an orthogonal decomposition of the underlying regression function, with an arbitrarily chosen parametric family, under a special inner product structure arising from the bias formula of the estimator. It is shown that the proposed method entails reduction in the constant factor of the leading bias of the existing method while it retains the same first-order variance. These theoretical findings are confirmed in Monte Carlo experiments.

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