IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v54y2013i3p827-837.html
   My bibliography  Save this article

On a new interpretation of the sample variance

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-012-0465-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00362-012-0465-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sen, Amartya, 1997. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198292975.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Andonie, Costel & Kuzmics, Christoph & Rogers, Brian W., 2019. "Efficiency-based measures of inequality," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 60-69.
    2. David Bravo & Dante Contreras & Sergio Urzúa, 2002. "Poverty and Inequality in Chile 1990-1998: Learning from Microeconomic Simulations," Working Papers wp198, University of Chile, Department of Economics.
    3. Juan Luis Londoño & Miguel Székely, 2000. "Persistent Poverty and Excess Inequality: Latin America, 1970-1995," Journal of Applied Economics, Universidad del CEMA, vol. 3, pages 93-134, May.
    4. Cem Baslevent & Meltem Dayoglu, 2005. "The Effect of Squatter Housing on Income Distribution in Urban Turkey," Urban Studies, Urban Studies Journal Limited, vol. 42(1), pages 31-45, January.
    5. Merz, Joachim & Rathjen, Tim, 2011. "Intensity of Time and Income Interdependent Multidimensional Poverty: Well-Being and Minimum 2DGAP – German Evidence," IZA Discussion Papers 6022, Institute of Labor Economics (IZA).
    6. Ada Ferrer-i-Carbonell & Bernard Van Praag, 2003. "Income Satisfaction Inequality and its Causes," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 1(2), pages 107-127, August.
    7. Tugce, Cuhadaroglu, 2013. "My Group Beats Your Group: Evaluating Non-Income Inequalities," SIRE Discussion Papers 2013-49, Scottish Institute for Research in Economics (SIRE).
    8. Hendrik Thiel & Stephan L. Thomsen, 2015. "Individual Poverty Paths and the Stability of Control-Perception," SOEPpapers on Multidisciplinary Panel Data Research 794, DIW Berlin, The German Socio-Economic Panel (SOEP).
    9. repec:pru:wpaper:8 is not listed on IDEAS
    10. Reiko Gotoh & Naoki Yoshihara, 2018. "Securing basic well-being for all," Review of Social Economy, Taylor & Francis Journals, vol. 76(4), pages 422-452, October.
    11. Simone Schneider, 2012. "Income Inequality and its Consequences for Life Satisfaction: What Role do Social Cognitions Play?," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 106(3), pages 419-438, May.
    12. Londoño, Juan Luis & Székely, Miguel, 1997. "Persistent Poverty and Excess Inequality: Latin America, 1970-1995," IDB Publications (Working Papers) 6092, Inter-American Development Bank.
    13. Vizard, Polly, 2005. "The contributions of Professor Amartya Sen in the field of human rights," LSE Research Online Documents on Economics 6273, London School of Economics and Political Science, LSE Library.
    14. Venkatasubramanian, Venkat & Luo, Yu & Sethuraman, Jay, 2015. "How much inequality in income is fair? A microeconomic game theoretic perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 435(C), pages 120-138.
    15. Satya R. Chakravarty & Pietro Muliere, 2003. "Welfare indicators: A review and new perspectives. 1. Measurement of inequality," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 457-497.
    16. Constantine Angyridis & Brennan Scott Thompson, 2016. "Negative income taxes, inequality and poverty," Canadian Journal of Economics, Canadian Economics Association, vol. 49(3), pages 1016-1034, August.
    17. Sabina Alkire & Maria Emma Santos, 2010. "Acute Multidimensional Poverty: A New Index for Developing Countries," Human Development Research Papers (2009 to present) HDRP-2010-11, Human Development Report Office (HDRO), United Nations Development Programme (UNDP).
    18. Alkire, Sabina & Santos, Maria Emma, 2014. "Measuring Acute Poverty in the Developing World: Robustness and Scope of the Multidimensional Poverty Index," World Development, Elsevier, vol. 59(C), pages 251-274.
    19. Marta Santagata & Enrico Ivaldi & Riccardo Soliani, 2019. "Development and Governance in the Ex-Soviet Union: An Empirical Inquiry," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 141(1), pages 157-190, January.
    20. Boris Branisa & Adriana Cardozo, 2009. "Regional Growth Convergence in Colombia Using Social Indicators," Ibero America Institute for Econ. Research (IAI) Discussion Papers 195, Ibero-America Institute for Economic Research.
    21. Benoit Decerf, 2021. "Combining absolute and relative poverty: income poverty measurement with two poverty lines," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(2), pages 325-362, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:54:y:2013:i:3:p:827-837. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.