Abstract
Consider the problem of estimating the mean of a normal population when independent samples from this as well as a second normal population are available. Pre-test estimators which combine the two sample means if a test of the hypothesis of equal population means accepts but otherwise use only the first sample mean, are compared to limited translation estimators which are derived in the spirit of Bickel (1984, Ann. Statist., 12, 864–879) (we also cover the cases of unknown variances). Our conclusion is that if the accuracy with which the second population mean can be estimated is of the same or better order of magnitude as teh accuracy with which the first can be estimated, then the limited translation estimators largely dominate the pre-test estimators in terms of mean square error loss.
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References
Bickel, P. J. (1984). Parametric robustness: small biases can be worthwhile, Ann. Statist., 12, 864–879.
Efron, B. and Morris, C. (1971). Limiting the risk of Bayes and empirical Bayes estimators—Part I: the Bayes case, J. Amer. Statist. Assoc., 66, 807–815.
Graybill, F. A. and Deal, R. B. (1959). Combining unbiased estimators, Biometrics, 15, 543–550.
Ohtani, K. (1987). On the use of the Graybill-Deal estimator when two normal population means may not be common, Comm. Statist. B—Simulation Comput., 16, 855–870.
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This research was supported by grants from the FRD of the CSIR of South Africa.
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Venter, J.H., Steel, S.J. Estimation of two normal means which may be common. Ann Inst Stat Math 42, 51–64 (1990). https://doi.org/10.1007/BF00050778
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DOI: https://doi.org/10.1007/BF00050778