A unified approach to estimation of noncentrality parameters, the multiple correlation coefficient, and mixture models

Abstract

We consider a class of mixture models for positive continuous data and the estimation of an underlying parameter θ of the mixing distribution. With a unified approach, we obtain classes of dominating estimators under squared error loss of an unbiased estimator, which include smooth estimators. Applications include estimating noncentrality parameters of chi-square and F-distributions, as well as ρ²/(1 − ρ²), where ρ is amultivariate correlation coefficient in a multivariate normal set-up. Finally, the findings are extended to situations, where there exists a lower bound constraint on θ.