On the umvu estimators after using a normalizing transformation |
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Authors: | Huaixiang Li DB Owen |
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Institution: | 1. Chesapeake Biological Lab , University of Maryland , Solomons, MD, 20688;2. Dept. of Stat. Science , Southern Methodist Univ , Dallas, TX, 75275-0332 |
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Abstract: | The conditional distribution given complete sufficient statistics is used along with the Rao-Blackwell theorem to obtain uniformly minimum variance unbiased (UMVU) estimators after a transformation to normality has been applied to data. The estimators considered are for the mean, the variance and the cumulative distribution of the original non-normal data. Previous procedures to obtain UMVU estimators have used Laplace transforms, Taylor expansions and the jackknife. An integration method developed in this paper requires only integrability of the normalizing transformation function. This method is easy to employ and it is always possible to obtain a numerical result. |
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Keywords: | Uniformly minimum variance unbiased estimators Rao-Blackwell theorem Estimators for mean variance and cumulative distribution function |
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