Comments and Queries Comment on “An Estimation Procedure for Mixtures of Distributions” by Choi and Bulgren
Peter D. M. MacDonald · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1971
Summary Choi and Bulgren's (1968) estimator for the mixing measure of a mixture of known distributions is biased in small samples; a variant of their estimator has a much smaller bias, and a smaller mean squared error, for mixtures of normal distributions differing in mean. The maximum-likelihood estimator is shown to be more computable than Choi and Bulgren suggest. Estimation is much more difficult when the component distributions are unknown; for example, a mixture of two normal components has five parameters, but no more than four may be estimated when the components are close together.