Estimating the mixing proportion in a semiparametric mixture model

In this paper, we investigate methods of estimating the mixing proportion in the case when one of the probability densities is not specified analytically in a mixture model. The methodology we propose is motivated by a sequential clustering algorithm. After a sequential clustering algorithm finds the center of a cluster, the next step is to identify observations belonging to that cluster. If we assume that the center of the cluster is known and that the distribution of observations not belonging to the cluster is unknown, the problem of identifying observations in the cluster is similar to the problem of estimating the mixing proportion in a special two-component mixture model. The mixing proportion can be considered as the proportion of observations belonging to the cluster. We propose two estimators for parameters in the model and compare the performance of these two estimators in several different cases.