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On the estimation of a variance ratio. (English) Zbl 0664.62021
The estimation of the ratio of two independent normal variances is considered under scale invariant squared error loss function, when the means are unknown. The best invariant estimator is shown to be inadmissible. Two new classes of improved estimators are obtained, one by extending C. Stein [Ann. Inst. Stat. Math. 16, The 20th Anniv. Vol. Part I, 155-160 (1964; Zbl 0144.414)] and the other by extending L. D. Brown [Ann. Math. Stat. 39, 29-48 (1968; Zbl 0162.499)]. Numerical studies are presented to indicate the percent improvements in risk.

62F10 Point estimation
62C15 Admissibility in statistical decision theory
62C99 Statistical decision theory
Full Text: DOI
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