Mathematical Methods of Statistics

, Volume 26, Issue 2, pp 134–148 | Cite as

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

  • T. KubokawaEmail author
  • É. MarchandEmail author
  • W. E. StrawdermanEmail author


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.


estimation lower bounded parameter mixtures multiple correlation coefficient noncentrality parameter 

2000 Mathematics Subject Classification

62C20 62C86 62F10 62F15 62F30 


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© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Dept. of EconomicsUniv. of TokyoTokyoJapan
  2. 2.Univ. de Sherbrooke, Départ. de math.Sherbrooke QcCanada
  3. 3.Dept. of Statist. and Biostatist.Rutgers Univ.PiscatawayUSA

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