An unbiased minimum distance estimator of the proportion parameter in a mixture of two normal distributions

An estimator that minimizes an L2 distance used in studies of estimation of the location parameter is shown here to give an explicit formulation for the estimator of proportion in a mixture of two normal distributions when other parameters are known. This can prove to be an advantage over other minimum distance methods and the maximum likelihood estimator. Monte Carlo simulation demonstrates this and highlights good small sample behaviour of the estimator. It is shown that the estimator is also qualitatively robust both empirically and asymptotically, the latter being evidenced by the existence of a Fréchet derivative.