Multiresolution approximation and consistent estimation of a multivariate density function

Abstract

In this paper we extend multiresolution analysis structures on R^q to approximate multivariate probability density functions. We propose a consistent estimator for a multivariate multiresolution approximation (MMR) of a multivariate pdf. And we also develop an algorithm to estimate the MMR pdf that behaves well when handling big data. This algorithm performs better, in terms of running time, than traditional optimization algorithms. For large samples, the estimations are as good as those obtained by maximum likelihood. Numerical results are provided to illustrate the method.