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On a new interpretation of the sample variance

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  • Nitis Mukhopadhyay
  • Bhargab Chattopadhyay

Abstract

It may not be an overstatement that one of the most widely reported measures of variation involves S 2 , the sample variance, which is also well-known to be alternatively expressed in the form of an U statistic with a symmetric kernel of degree 2 whatever be the population distribution function. We propose a very general new approach to construct unbiased estimators of a population variance by U statistics with symmetric kernels of degree higher than two. Surprisingly, all such estimators ultimately reduce to S 2 (Theorem 3.1). While Theorem 3.1 is interesting and novel in its own right, it leads to a newer interpretation of S 2 that is much broader than what is known in the statistical literature including economics, actuarial mathematics, and mathematical finance. Copyright Springer-Verlag 2013

Suggested Citation

  • Nitis Mukhopadhyay & Bhargab Chattopadhyay, 2013. "On a new interpretation of the sample variance," Statistical Papers, Springer, vol. 54(3), pages 827-837, August.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:3:p:827-837
    DOI: 10.1007/s00362-012-0465-y
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    1. Sen, Amartya, 1997. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198292975.
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