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.
J. O. Berger, A. Philippe, and C. P. Robert, “Estimation of Quadratic Functions: Noninformative Priors for Noncentrality Parameters”, Statist. Sinica 8, 359–375 (1998).MathSciNetzbMATHGoogle Scholar
L. Brown, I. Johnstone, and B. MacGibbon, “Variation Diminishing Transfromations: A Direct Approach to Total Positivity and Its Statistical Applications”, J. Amer. Statist. Assoc. 76, 824–832 (1981).MathSciNetCrossRefzbMATHGoogle Scholar
P. L. Leung and R. J. Muirhead, “Estimation of Parameter Matrices and Eigenvalues in MANOVA and Canonical Correlation Analysis”, Ann. Statist. 15, 1651–1666 (1987).MathSciNetCrossRefzbMATHGoogle Scholar
M. Lo and P. L. Leung, “Decision Theoretic Estimation of Functions of the Canonical Correlation Coefficients”, Commun. Statist.–Theory Methods 25, 1985–1995 (1996).MathSciNetCrossRefzbMATHGoogle Scholar
É. Marchand and W. E. Strawderman, “On Improving on the Minimum Risk Equivariant Estimator of a Location Parameter Which is Constrained to an Interval or a Half-Interval”, Ann. Inst. Statist. Math. 57, 129–143 (2005).MathSciNetCrossRefzbMATHGoogle Scholar
P. Y.-S. Shao and W. E. Strawderman, “Improving on the Positive Part of the UMVUE of a Noncentrality Parameter of a Noncentral Chi-Square Distribution”, J. Multivariate Anal. 53, 52–66 (1995).MathSciNetCrossRefzbMATHGoogle Scholar