  Maximum likelihood estimators are proposed for the parameters and the
densities in a semiparametric density ratio model in which the nonparametric
baseline density is approximated by the Bernstein polynomial model. The EM
algorithm is used to obtain the maximum approximate Bernstein likelihood
estimates. Simulation study shows that the performance of the proposed method
is much better than the existing ones. The proposed method is illustrated by
real data examples. Some asymptotic results are also presented and proved.
