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Precision of Individual Estimators in Simultaneous Estimation of Parameters
C. Radhakrishna Rao and Nobuo Shinozaki
Vol. 65, No. 1 (Apr., 1978), pp. 23-30
Stable URL: http://www.jstor.org/stable/2335272
Page Count: 8
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Biases and mean squared errors of estimators of individual parameters are obtained for Stein type estimators of a vector parameter. It is known that for such estimators the average mean squared error over the different parameters under estimation is smaller than that for the usual unbiased estimators. However, such a property may not hold for the mean squared error of any individual estimator for the corresponding parameter. It is found that when a number of parameters are estimated simultaneously by Stein type estimators, some individual estimators have larger mean squared error than those of the usual unbiased estimators and others less. For several combinations of number of parameters and their mean and standard deviation, the range of parameter values for which the Stein type is better has been computed.
Biometrika © 1978 Biometrika Trust