  A new maximum likelihood method for deconvoluting a continuous density with a
positive lower bound on a known compact support in additive measurement error
models with known error distribution using the approximate Bernstein type
polynomial model, a finite mixture of specific beta distributions, is proposed.
The change-point detection method is used to choose an optimal model degree.
Based on a contaminated sample of size $n$, under an assumption which is
satisfied, among others, by the generalized normal error distribution, the
optimal rate of convergence of the mean integrated squared error is proved to
be $k^{-1}\mathcal{O}(n^{-1+1/k}\log^3 n)$ if the underlying unknown density
has continuous $2k$th derivative with $k>1$. Simulation shows that small sample
performance of our estimator is better than the deconvolution kernel density
estimator. The proposed method is illustrated by a real data application.
