The doubly smoothed maximum likelihood estimation for location-shifted semiparametric mixtures

Finite mixture of a location family of distributions are known to be identifiable if the component distributions are common and symmetric. In such cases, several methods have been proposed for estimating both the symmetric component distribution and the model parameters. In this paper, we propose a new estimation method using the doubly smoothed maximum likelihood, which can effectively eliminate potential biases while maintaining a high efficiency. Some numerical examples are presented to demonstrate the performance of the proposed method.