Statistical Analysis from the Fourier Integral Theorem
Abstract
Taking the Fourier integral theorem as our starting point, in this paper we focus on natural Monte Carlo and fully nonparametric estimators of multivariate distributions and conditional distribution functions. We do this without the need for any estimated covariance matrix or dependence structure between variables. These aspects arise immediately from the integral theorem. Being able to model multivariate data sets using conditional distribution functions we can study a number of problems, such as prediction for Markov processes, estimation of mixing distribution functions which depend on covariates, and general multivariate data. Estimators are explicit Monte Carlo based and require no recursive or iterative algorithms.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.06608
 Bibcode:
 2021arXiv210606608H
 Keywords:

 Statistics  Methodology;
 Computer Science  Machine Learning;
 Statistics  Computation;
 Statistics  Machine Learning
 EPrint:
 20 pages, 10 figures