Semiparametric mixture: Continuous scale mixture approach

In this article, we propose a new estimation procedure for a class of semiparametric mixture models that is a mixture of unknown location-shifted symmetric distributions. The proposed method assumes that the nonparametric symmetric distribution falls in a rich class of continuous normal scale mixture distributions. With this new modeling approach, we can suitably avoid the misspecification problem in traditional parametric mixture models. In addition, unlike some existing semiparametric methods, the proposed method does not require any modification or smoothing of the likelihood as it can directly estimate parametric and nonparametric components simultaneously in the model. Furthermore, the proposed parameter estimates are robust against outliers. The estimation algorithms are introduced and numerical studies are conducted to examine the finite sample performance of the proposed procedure and to compare it with other existing methods.