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.

翻译：半对称密度率模型的参数和密度提出了最大可能性估计值,该模型的非参数基线密度被伯恩斯坦多元模型所近似。EM算法用于获取最高接近伯恩斯坦概率估计值的最大值。模拟研究表明,拟议方法的性能比现有方法好得多。拟议方法用真实数据实例加以说明。还提出和证明了一些无参数的结果。