Advances and Applications in Statistics
Volume 13, Issue 2, Pages 241 - 256
(December 2009)
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ESTIMATION OF UNIVARIATE NORMAL MEAN USING p-VALUE
Md. Enamul Kabir (Australia) and Shahjahan Khan (Australia)
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Abstract: This paper estimates the mean of a normal distribution in presence of non-sample prior information regarding the value of the mean. We define the unrestricted estimator (UE), restricted estimator (RE), p-value based restricted estimator (PRE) and p-value based preliminary test estimator (PPTE) based on the sample, prior information and p-value of an appropriate test. The relative performance of these estimators is studied on the basis of bias and mean square error (MSE) criteria. Both analytical and graphical comparisons are pursued. If the p-value is reasonably small, the PRE uniformly overperforms the UE and PPTE, regardless of the level of significance. |
Keywords and phrases: unrestricted estimator (UE), restricted estimator (RE), p-value, p-value based restricted estimator (PRE), p-value based preliminary test estimator (PPTE), mean square error (MSE). |
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