, Volume 54, Issue 3, pp 827837
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 wellknown 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.
Keywords
Actuarial mathematics Economic theory Gini’s mean difference Mathematical finance Sample variance U statisticsMathematics Subject Classification (2000)
62G05 62G99 62F10 Title
 On a new interpretation of the sample variance
 Journal

Statistical Papers
Volume 54, Issue 3 , pp 827837
 Cover Date
 201308
 DOI
 10.1007/s003620120465y
 Print ISSN
 09325026
 Online ISSN
 16139798
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Actuarial mathematics
 Economic theory
 Gini’s mean difference
 Mathematical finance
 Sample variance
 U statistics
 62G05
 62G99
 62F10
 Industry Sectors
 Authors

 Nitis Mukhopadhyay ^{(1)}
 Bhargab Chattopadhyay ^{(1)}
 Author Affiliations

 1. Department of Statistics, University of Connecticut, UBox 4120, Storrs, CT, 062694120, USA