Inferences for Two-Component Mixture Models with Stochastic Dominance
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2018-01-18
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Abstract
In this thesis, we studied a two-component nonparametric mixture model with a stochastic dominance constraint, which is a model that arises naturally from genetic studies. For this model, we proposed and studied nonparametric estimation based on cumulative distribution functions (c.d.f.s) and maximum likelihood estimation (MLE) through multinomial approximation. In order to incorporate the stochastic dominance constraint, we introduced a semiparametric model structure for which we proposed and investigated both MLE and minimum Hellinger distance estimation (MHDE). We also proposed a hypothesis testing to test the validity of the semiparametric model. For the proposed methods, we investigated their asymptotic properties such as consistency and asymptotic normality theoretically and through simulation studies. Our numerical studies demonstrated that (1) all the proposed estimation methods work well; (2) the semiparametric model structure incorporates nicely the stochastic dominance constraint and thus the MLE and MHDE based on it are superior in terms of efficiency than the two estimation techniques that do not use this model structure; (3) the MHDE is much more robust than the MLE. To demonstrate the use of these methods, we applied them to several real data including publicly available grain data (Smith et al., 1986) and malaria data (Vonatsou et al., 1998).
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Abedin, T. (2018). Inferences for Two-Component Mixture Models with Stochastic Dominance (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.