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1999•Scandinavian Journal of StatisticsRequires access

Multiple Kernel Procedure: an Asymptotic Support

Philippe Vieu

Open publisher page 7 citations

Abstract

ABSTRACT. This paper deals with kernel non‐parametric estimation. The multiple kernel method, as proposed by Berlinet (1993), consists in choosing both the smoothing parameter and the order of the kernel function. In this paper we follow this general idea, and the selection is carried out by a combination of plug‐in and cross‐validation techniques. In a first attempt we give an asymptotic optimality theorem which is stated in a general unifying setting that includes many curve estimation problems. Then, as an illustration, it will be seen how this behaves in both special cases of kernel density and kernel regression estimation.

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What this paper is about

ABSTRACT. This paper deals with kernel non‐parametric estimation. The multiple kernel method, as proposed by Berlinet (1993), consists in choosing both the smoothing parameter and the order of the kernel function. In this paper we follow this general idea, and the selection is carried out by a combination of plug‐in and cross‐validation techniques. In a first attempt we give an asymptotic optimality theorem which is stated in a general unifying setting that includes many curve estimation problems. Then, as an illustration, it will be seen how this behaves in both special cases of kernel density and kernel regression estimation.

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Available abstract

ABSTRACT. This paper deals with kernel non‐parametric estimation. The multiple kernel method, as proposed by Berlinet (1993), consists in choosing both the smoothing parameter and the order of the kernel function. In this paper we follow this general idea, and the selection is carried out by a combination of plug‐in and cross‐validation techniques. In a first attempt we give an asymptotic optimality theorem which is stated in a general unifying setting that includes many curve estimation problems. Then, as an illustration, it will be seen how this behaves in both special cases of kernel density and kernel regression estimation.

Key concepts: Mathematics, Kernel smoother, Variable kernel density estimation, Kernel (algebra), Kernel density estimation, Kernel embedding of distributions, Applied mathematics, Kernel regression

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