On a new interpretation of the sample variance

Nitis Mukhopadhyay () and Bhargab Chattopadhyay ()

Statistical Papers, 2013, vol. 54, issue 3, 827-837

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

Keywords: Actuarial mathematics; Economic theory; Gini’s mean difference; Mathematical finance; Sample variance; U statistics; 62G05; 62G99; 62F10 (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1007/s00362-012-0465-y (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stpapr:v:54:y:2013:i:3:p:827-837

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-012-0465-y

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

More articles in Statistical Papers from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().