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On Bessel’s Correction: Unbiased Sample Variance, the “Bariance,†and a Novel Runtime-Optimized Estimator

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  • Felix Reichel

Abstract

Bessel’s correction adjusts the denominator in the sample variance formula from n to n −1 to produce an unbiased estimator for the population variance. This paper includes rigorous derivations, geometric interpretations, and visualizations. It then introduces the concept of “bariance,†an alternative pairwise distances intuition of sample dispersion without an arithmetic mean. Finally, we address practical concerns raised in Rosenthal’s article [1] advocating the use of n-based estimates from a more holistic MSE-based viewpoint for pedagogical reasons and in certain practical contexts. Finally, the empirical part using simulation reveals that the run-time of estimating population variance can be shortened when using an algebraically optimized “bariance“ approach to estimate an unbiased variance.

Suggested Citation

  • Felix Reichel, 2025. "On Bessel’s Correction: Unbiased Sample Variance, the “Bariance,†and a Novel Runtime-Optimized Estimator," Economics working papers 2025-06, Department of Economics, Johannes Kepler University Linz, Austria.
    • Handle: RePEc:jku:econwp:2025-06
    Note: English
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    References listed on IDEAS

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    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Smyth Gordon K, 2004. "Linear Models and Empirical Bayes Methods for Assessing Differential Expression in Microarray Experiments," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-28, February.
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    More about this item

    Keywords

    Unbiased sample variance; Runtime-optimized linear unbiased sample variance estimators;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General

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