# Multivariate density estimation by neural networks

Nonparametric method for multivariate density estimation using neural networks

In this paper, a parameter-free method is proposed to determine the probability density function of multi-dimensional data sources. A neural network is used to approximate the empirical cumulative distribution function. The corresponding probability density is then obtained by determining the (partial) derivatives of the network. Existing methods in the literature can be used to approximate univariate continuous probability distributions only.

The methodology in this paper can be used to estimate multivariate continuous and discrete probability distributions. Through simulations, it is shown how the methodology performs for a probability mixture of normal distributions, a probability mixture of generalised extreme value distributions, a probability mixture of Poisson distributions, bivariate Poisson distribution, bivariate normal distribution and a trivariate normal distribution.