  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.
