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Multiple Kernel Procedure: an Asymptotic Support
Author(s) -
Vieu Philippe
Publication year - 1999
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00137
Subject(s) - mathematics , kernel smoother , variable kernel density estimation , kernel (algebra) , kernel density estimation , kernel embedding of distributions , kernel regression , kernel method , smoothing , kernel principal component analysis , polynomial kernel , mathematical optimization , nonparametric regression , statistics , radial basis function kernel , regression , artificial intelligence , computer science , combinatorics , support vector machine , estimator
. 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.