A two-component nonparametric mixture model with stochastic dominance

In this paper, we introduced a new two-component nonparametric mixture model with a stochastic dominance constraint, a model arising naturally from many genetic studies. For this model, we proposed and studied two estimations. The first one is based on cumulative distribution functions with use of the stochastic dominance inequality, while the second one is a maximum likelihood estimation of the multinomial approximation of the model. For both methods, we not only proved their consistency but also examined their finite-sample performance through simulation studies. Our numerical studies showed that both methods work equivalently well. To demonstrate their implementation, we applied them to two real datasets.