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 ρ ²/(1 − ρ ²), 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.

中文翻译：

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估计非中心参数，多重相关系数和混合模型的统一方法

我们考虑一类用于正连续数据的混合模型以及混合分布的基础参数θ的估计。通过统一的方法，我们获得了无偏估计量平方误差损失下的主导估计量类别，其中包括光滑估计量。应用包括估计卡方和的noncentrality参数˚F -distributions，以及ρ ² /（1 - ρ ²），其中ρ是在一个多变量正态分布的建立amultivariate相关系数。最后，将发现扩展到对θ存在下界约束的情况。