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Double shrinkage estimation of ratio of scale parameters. (English) Zbl 0804.62026
Summary: The problems of estimating ratio of scale parameters of two distributions with unknown location parameters are treated from a decision-theoretic point of view. The paper provides the procedures improving on the usual ratio estimator under strictly convex loss functions and the general distributions having monotone likelihood ratio properties.
In particular, double shrinkage improved estimators which utilize both estimators of two location parameters are presented. Under order restrictions on the scale parameters, various improvements for estimation of the ratio and the scale parameters are also considered. These results are applied to normal, lognormal, exponential and Pareto distributions. Finally, a multivariate extension is given for the ratio of covariance matrices.

MSC:
 62F10 Point estimation 62H12 Estimation in multivariate analysis
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References:
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