Estimating quantiles of several normal populations with a common mean |
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Authors: | Manas Ranjan Tripathy Somesh Kumar Adarsha Kumar Jena |
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Affiliation: | 1. Department of Mathematics, National Institute of Technology Rourkela, Rourkela, India;2. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, India |
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Abstract: | Suppose we have k( ? 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 Kumar and Tripathy (2011 Kumar, S., Tripathy, M.R. (2011). Estimating quantiles of normal populations with a common mean. Commun. Stat. - Theory Methods 40:2719–2736.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) for k = 2 to a general k( ? 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. |
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Keywords: | Affine equivariant estimators common mean inadmissibility location equivariant estimators quadratic loss function quantile estimation relative risk performance. |
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