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Estimating quantiles of several normal populations with a common mean. (English) Zbl 1391.62011

Summary: Suppose we have \(k\) \((\geq 2)\) normal populations with a common mean and possibly different variances. The problem of estimation of quantile of the first population is considered with respect to a quadratic loss function. In this paper, we have generalized the inadmissibility results obtained by the second and the first author [ibid. 40, No. 15, 2719–2736 (2011; Zbl 1216.62033)] for \(k=2\) to a general \(k\) \((\geq 2)\). Moreover, a massive simulation study has been done in order to numerically compare the risk values of various proposed estimators for the cases \(k=3\) and \(k=4\) and recommendations are made for the use of estimators under certain situations.

MSC:

62C15 Admissibility in statistical decision theory
62C07 Complete class results in statistical decision theory
62F10 Point estimation
62P10 Applications of statistics to biology and medical sciences; meta analysis

Citations:

Zbl 1216.62033
Full Text: DOI