In this work, we studied a two-component mixture model with stochastic dominance constraint, a model arising naturally from many genetic studies. To model the stochastic dominance, we proposed a semiparametric modelling of the log of density ratio. More specifically, when the log of the ratio of two component densities is in a linear regression form, the stochastic dominance is immediately satisfied. For the resulting semiparametric mixture model, we proposed two estimators, maximum empirical likelihood estimator (MELE) and minimum Hellinger distance estimator (MHDE), and investigated their asymptotic properties such as consistency and normality. In addition, to test the validity of the proposed semiparametric model, we developed Kolmogorov–Smirnov type tests based on the two estimators. The finite-sample performance, in terms of both efficiency and robustness, of the two estimators and the tests were examined and compared via both thorough Monte Carlo simulation studies and real data analysis.

在这项工作中，我们研究了具有随机优势约束的双组分混合模型，该模型自然产生于许多遗传研究。为了对随机优势进行建模，我们提出了密度比对数的半参数建模。更具体地说，当两个成分密度之比的对数为线性回归形式时，立即满足随机优势。对于由此产生的半参数混合模型，我们提出了两个估计量，即最大经验似然估计量 (MELE) 和最小 Hellinger 距离估计量 (MHDE)，并研究了它们的渐近特性，例如一致性和正态性。此外，为了测试所提出的半参数模型的有效性，我们开发了基于两个估计量的 Kolmogorov–Smirnov 类型检验。有限样本性能，