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...

The elegant Hartley--Ross inequality on the absolute bias ratio (ABR [reverse not equivalent] Bias /S.E.) of a ordinary ratio estimator is here generalized to that of a separate ratio estimator with stratified sampling. It is shown that, as long as the numerators and denominators used to form...