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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References
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Wencheko, E., Chipoyera, H.W. Estimation of the variance when kurtosis is known. Stat Papers 50, 455–464 (2009). https://doi.org/10.1007/s00362-007-0084-1
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DOI: https://doi.org/10.1007/s00362-007-0084-1