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Fourier series approximation of separable models. (English) Zbl 1058.62034

The authors consider Fourier series estimators of additive nonparametric models. They describe a Fourier direct separation method to build an estimator of the regression curve, both for uniform and random data. The convergence and asymptotic optimality of this method is proved. Many numerical tests are presented. The computational efficiency of this procedure is compared with other known methods.

MSC:

62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
65C60 Computational problems in statistics (MSC2010)
65T40 Numerical methods for trigonometric approximation and interpolation
42B05 Fourier series and coefficients in several variables

Software:

FUNFITS; S-PLUS; R
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Full Text: DOI

References:

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