Estimation of the variance when kurtosis is known |
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Authors: | Eshetu Wencheko Honest W Chipoyera |
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Institution: | (1) Department of Statistics, Addis Ababa University, P. O. Box 1176, Addis Ababa, Ethiopia;(2) Department of Statistics and Operations Research, University of Limpopo, P. Bag X1106, Sovenga, 0727, Republic of South Africa |
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Abstract: | The unbiased estimator of a population variance σ2, S
2 has traditionally been overemphasized, regardless of sample size. In this paper, alternative estimators of population variance
are developed. These estimators are biased and have the minimum possible mean-squared error and we define them as the “minimum mean-squared error biased estimators” (MBBE)]. The comparative merit of these estimators over the unbiased estimator is explored using relative efficiency (RE)
(a ratio of mean-squared error values). It is found that, across all population distributions investigated, the RE of the
MBBE is much higher for small samples and progressively diminishes to 1 with increasing sample size. The paper gives two applications
involving the normal and exponential distributions. |
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Keywords: | Kurtosis Minimum mean-squared error Biased estimator Relative efficiency Unbiased sample variance |
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