Regular Article

Statistical Papers

, Volume 54, Issue 3, pp 827-837

First online:

On a new interpretation of the sample variance

  • Nitis MukhopadhyayAffiliated withDepartment of Statistics, University of Connecticut Email author 
  • , Bhargab ChattopadhyayAffiliated withDepartment of Statistics, University of Connecticut

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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.


Actuarial mathematics Economic theory Gini’s mean difference Mathematical finance Sample variance U statistics

Mathematics Subject Classification (2000)

62G05 62G99 62F10