Empirical Likelihood Estimation of Censored Mixture Models

In this paper, a mixture model is estimated by the empirical likelihood (EL) approach. The functional delta method is implemented to exploit asymptotic properties of the estimator. EL constructs a weighted empirical process that converges to a Gaussian process and its estimator, with additional assumptions, converges a normal distribution with an asymptotic efficient covariance matrix. This approach can be extended to the censoring case. With the self-consistency restriction, EL preserves strong consistency and its empirical process is Gaussian.