Multivariate wavelet kernel regression method
Résumé
The purpose of this paper is to introduce a new penalized multivariate nonparametric regression method, in the framework of wavelet decomposition. We call this method the wavelet kernel ANOVA (WK-ANOVA), which is a wavelet based reproducing kernel Hilbert space (RKHS) method with the penalty equal to the sum of blockwise RKHS norms. This method does not require design points to be equispaced or of dyadic size thus making high-dimensional wavelet estimation feasible. We also introduce a new iterative shrinkage algorithm to solve the nonegative garrote optimization problem resulting in the variable selection step. Numerical experiments on several test functions show that the WK-ANOVA provides competitive results compared to other standard methods.
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