an:00681365
Zbl 0804.62026
Kubokawa, Tatsuya
Double shrinkage estimation of ratio of scale parameters
EN
Ann. Inst. Stat. Math. 46, No. 1, 95-116 (1994).
00021812
1994
j
62F10 62H12
ratio of variances; shrinkage estimation; inadmissibility; Stein's truncated rule; noncentral chi-square distributions; estimation of ordered scale parameters; estimating ratio of scale parameters; unknown location; strictly convex loss functions; monotone likelihood ratio properties; double shrinkage improved estimators; order restrictions; normal; lognormal; exponential; Pareto distributions; ratio of covariance matrices
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.