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Estimation of order restricted standard deviations of normal populations with a common mean

The present paper deals with estimating standard deviations of two normal populations with a common mean and ordered variances. We propose a class of improved estimators of the standard deviations under the quadratic loss function. Considering k normal populations with a common mean and ordered variances, we establish inadmissibility results of the affine and scale equivariant estimators of the smallest standard deviation and derive its improved estimators. Simulation studies are performed to compare the risks of the improved estimators with the existing estimators. Two illustrative examples are presented as applications of the proposed estimators.