Bernstein Polynomial Model for Grouped Continuous Data

TL;DR

This paper introduces a Bernstein polynomial approach for estimating univariate density functions from grouped data, utilizing an EM algorithm for coefficient estimation and a change-point method for selecting polynomial degree, with proven convergence properties.

Contribution

It presents a novel Bernstein polynomial model for grouped data density estimation, including an EM algorithm for coefficient estimation and a change-point method for degree selection.

Findings

The method achieves almost parametric convergence rate.

Simulation studies show competitive performance.

Application to real data demonstrates practical utility.

Abstract

Grouped data are commonly encountered in applications. The Bernstein polynomial model is proposed as an approximate model in this paper for estimating a univariate density function based on grouped data. The coefficients of the Bernstein polynomial, as the mixture proportions of beta distributions, can be estimated using an EM algorithm. The optimal degree of the Bernstein polynomial can be determined using a change-point estimation method. The rate of convergence of the proposed density estimate to the true density is proved to be almost parametric by an acceptance-rejection arguments used in Monte Carlo method. The proposed method is compared with some existing methods in a simulation study and is applied to a real dataset.