Estimating quantiles of several normal populations with a common mean

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) 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.

KEYWORDS:

• Affine equivariant estimators
• common mean
• inadmissibility
• location equivariant estimators
• quadratic loss function
• quantile estimation
• relative risk performance.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62C15
• 62F10
• 62C07

Acknowledgments

The authors would like to thank the anonymous referee and the editor for their valuable suggestions and comments which have improved the manuscript.

Funding

Manas Ranjan Tripathy would like to thank DST (SERB), [SR/FTP/MS-037/2012 dated 4/10/2013] New Delhi, India, for providing financial support.