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Recursive bias estimation for multivariate regression smoothers. (English) Zbl 1305.62162
Summary: This paper presents a practical and simple fully nonparametric multivariate smoothing procedure that adapts to the underlying smoothness of the true regression function. Our estimator is easily computed by successive application of existing base smoothers (without the need of selecting an optimal smoothing parameter), such as thin-plate spline or kernel smoothers. The resulting smoother has better out of sample predictive capabilities than the underlying base smoother, or competing structurally constrained models (MARS, GAM) for small dimension (\(3 \leq d \leq 7\)) and moderate sample size \(n \leq 1000\). Moreover our estimator is still useful when \(d > 10\) and to our knowledge, no other adaptive fully nonparametric regression estimator is available without constrained assumption such as additivity for example. On a real example, the Boston Housing Data, our method reduces the out of sample prediction error by \(20\%\). An R package ibr, available at CRAN, implements the proposed multivariate nonparametric method in R.

MSC:
62G07 Density estimation
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
Software:
R; ibr; CRAN
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