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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.

##### MSC:
 62F10 Point estimation 62C15 Admissibility in statistical decision theory 62C99 Statistical decision theory
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##### References:
 [1] Abramowitz, M.; Stegun, I., Handbook of mathematical functions, 1, (1965), Dover New York [2] Brewster, J.F.; Zidek, J., Improving on equivariant estimators, Ann. statist., 2, 21-38, (1974) · Zbl 0275.62006 [3] Brown, L.D., On the admissibility of invariant estimators of one or more location parameters, Ann. math. statist., 37, 1087-1136, (1966) · Zbl 0156.39401 [4] Brown, L.D., Inadmissibility of the usual estimators of scale parameters, Ann. math. statist., 39, 29-48, (1968) · Zbl 0162.49901 [5] Brown, L.D.; Fox, M., Admissibility in statistical problems involving a location or scale parameter, Ann. statist., 2, 807-814, (1974) · Zbl 0285.62004 [6] Stein, C., Inadmissibility of the usual estimator for the variance of a normal distribution with unknown Mean, Ann. inst. statist. math., 42, 385-388, (1964) [7] Strawderman, W.E., Minimax estimation of powers of the variance of normal population, Ann. statist., 2, 190-198, (1974) · Zbl 0309.62018
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