  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.
