Estimating Quantiles of Normal Populations with a Common Mean

Suppose independent random samples are available from two normal populations with a common mean and unequal variances. Estimation of a quantile of the first population is considered with respect to the quadratic loss. Some new estimators for the quantile are proposed using some previously known esti...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2011-08, Vol.40 (15), p.2719-2736
Main Authors: Kumar, Somesh, Tripathy, Manas Ranjan
Format: Article
Language:English
Subjects:
Common mean
Computer simulation
Equivariant estimators
Estimators
Exact sciences and technology
General topics
Inadmissibility
Linear inference, regression
Mathematical models
Mathematics
Minimaxity
Populations
Probability and statistics
Quantile estimation
Quantiles
Risk comparison
Samples
Sciences and techniques of general use
Statistics
Studies
Transformations
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Summary:Suppose independent random samples are available from two normal populations with a common mean and unequal variances. Estimation of a quantile of the first population is considered with respect to the quadratic loss. Some new estimators for the quantile are proposed using some previously known estimators of a common mean. Inadmissibility results are proved for estimators which are equivariant under affine and location groups of transformations. Risk values of various estimators of a quantile are compared numerically using a detailed simulation study.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2010.491587