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arXiv · 2108.12699

Density estimation in RKHS with application to Korobov spaces in high dimensions

Yoshihito Kazashi·Fabio Nobile
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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.

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Yoshihito Kazashi, Fabio Nobile. 2021-08-28. Density estimation in RKHS with application to Korobov spaces in high dimensions. https://doi.org/10.1137/22m147476x

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