Statistical Analysis from the Fourier Integral Theorem

• URL: http://arxiv.org/abs/2106.06608v1
• Date: Fri, 11 Jun 2021 20:44:54 GMT
• Title: Statistical Analysis from the Fourier Integral Theorem
• Authors: Nhat Ho, Stephen G. Walker
• Abstract summary: We look at Monte Carlo based estimators of conditional distribution functions. We study a number of problems, such as prediction for Markov processes. Estimators are explicit Monte Carlo based and require no iterative algorithms.
• Score: 9.619814126465206
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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