Maximum approximate Bernstein likelihood estimation in a two-sample semiparametric model

Maximum likelihood estimators are proposed for the parameters and the underlying 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. The proposed method is illustrated by two real data from medical research and is shown by simulation to have better performance than the existing ones. Some asymptotic results are also presented and proved.