  In this paper, we propose a variable selection method for general
nonparametric kernel-based estimation. The proposed method consists of
two-stage estimation: (1) construct a consistent estimator of the target
function, (2) approximate the estimator using a few variables by l1-type
penalized estimation. We see that the proposed method can be applied to various
kernel nonparametric estimation such as kernel ridge regression, kernel-based
density and density-ratio estimation. We prove that the proposed method has the
property of the variable selection consistency when the power series kernel is
used. This result is regarded as an extension of the variable selection
consistency for the non-negative garrote to the kernel-based estimators.
Several experiments including simulation studies and real data applications
show the effectiveness of the proposed method.
