Multivariate Smoothing via the Fourier Integral Theorem and Fourier Kernel
Statistics Theory
2021-01-01 v1 Methodology
Machine Learning
Statistics Theory
Abstract
Starting with the Fourier integral theorem, we present natural Monte Carlo estimators of multivariate functions including densities, mixing densities, transition densities, regression functions, and the search for modes of multivariate density functions (modal regression). Rates of convergence are established and, in many cases, provide superior rates to current standard estimators such as those based on kernels, including kernel density estimators and kernel regression functions. Numerical illustrations are presented.
Cite
@article{arxiv.2012.14482,
title = {Multivariate Smoothing via the Fourier Integral Theorem and Fourier Kernel},
author = {Nhat Ho and Stephen G. Walker},
journal= {arXiv preprint arXiv:2012.14482},
year = {2021}
}
Comments
58 pages, 6 figures