Density estimation in RKHS with application to Korobov spaces in high dimensions
Statistics Theory
2023-04-20 v4 Numerical Analysis
Numerical Analysis
Statistics Theory
Abstract
A kernel method for estimating a probability density function (pdf) from an i.i.d. sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined by a linear equation. An error analysis for the mean integrated squared error is established in a general reproducing kernel Hilbert space setting. The theory developed is then applied to estimate pdfs belonging to weighted Korobov spaces, for which a dimension independent convergence rate is established. Under a suitable smoothness assumption, our method attains a rate arbitrarily close to the optimal rate. Numerical results support our theory.
Keywords
Cite
@article{arxiv.2108.12699,
title = {Density estimation in RKHS with application to Korobov spaces in high dimensions},
author = {Yoshihito Kazashi and Fabio Nobile},
journal= {arXiv preprint arXiv:2108.12699},
year = {2023}
}