IDEAS home Printed from https://ideas.repec.org/p/zbw/faucse/882010.html
   My bibliography  Save this paper

Robustness properties of quasi-linear means with application to the Laspeyres and Paasche indices

Author

Listed:
  • Klein, Ingo
  • Ardelean, Vlad

Abstract

Li, Fang & Tian (1994) assert that special quasi-linear means should be preferred to the simple arithmetic mean for robustness properties. The strategy that is used to show robustness is completely detached from the concepts wellknown from the theory of robust statistics. Robustness of estimators can be verified with tools from robust statistics, e.g. the influence function or the breakdown point. On the other hand it seems that robust statistics is not interested in quasi-linear means. Therefore, we compute influence functions and breakdown points for quasi-linear means and show that these means are not robust in the sense of robust statistics if the generator is unbounded. As special cases we consider the Laspeyres, the Paasche and the Fisher indices.

Suggested Citation

  • Klein, Ingo & Ardelean, Vlad, 2012. "Robustness properties of quasi-linear means with application to the Laspeyres and Paasche indices," Discussion Papers 88/2010, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    • Handle: RePEc:zbw:faucse:882010
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/56059/1/689065132.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gamini Premaratne, 2005. "A Test for Symmetry with Leptokurtic Financial Data," Journal of Financial Econometrics, Oxford University Press, vol. 3(2), pages 169-187.
    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. Masayuki Hirukawa & Mari Sakudo, 2016. "Testing Symmetry of Unknown Densities via Smoothing with the Generalized Gamma Kernels," Econometrics, MDPI, vol. 4(2), pages 1-27, June.
    2. Fujiwara, Ippei & Körber, Lena Mareen & Nagakura, Daisuke, 2013. "Asymmetry in government bond returns," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3218-3226.
    3. Chi Zhang & Zhengning Pu & Qin Zhou, 2018. "Sustainable Energy Consumption in Northeast Asia: A Case from China’s Fuel Oil Futures Market," Sustainability, MDPI, vol. 10(1), pages 1-14, January.
    4. Lima Luiz Renato & Xiao Zhijie, 2010. "Testing Unit Root Based on Partially Adaptive Estimation," Journal of Time Series Econometrics, De Gruyter, vol. 2(1), pages 1-34, June.
    5. DiTraglia, Francis J. & Gerlach, Jeffrey R., 2013. "Portfolio selection: An extreme value approach," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 305-323.
    6. Esfandiar Maasoumi & Jeffrey Racine, 2009. "A Robust Entropy-Based Test of Asymmetry for Discrete and Continuous Processes," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 246-261.
    7. Stavroyiannis, S. & Makris, I. & Nikolaidis, V. & Zarangas, L., 2012. "Econometric modeling and value-at-risk using the Pearson type-IV distribution," International Review of Financial Analysis, Elsevier, vol. 22(C), pages 10-17.
    8. Francesco Lisi, 2007. "Testing asymmetry in financial time series," Quantitative Finance, Taylor & Francis Journals, vol. 7(6), pages 687-696.
    9. Zacharias Psaradakis & Marian Vavra, 2018. "Bootstrap Assisted Tests of Symmetry for Dependent Data," Working and Discussion Papers WP 5/2018, Research Department, National Bank of Slovakia.
    10. David Ashton & Mark Tippett, 2006. "Mean Reversion and the Distribution of United Kingdom Stock Index Returns," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 33(9‐10), pages 1586-1609, November.
    11. Carnero, M. Angeles & León, Angel & Ñíguez, Trino-Manuel, 2023. "Skewness in energy returns: estimation, testing and retain-->implications for tail risk," The Quarterly Review of Economics and Finance, Elsevier, vol. 90(C), pages 178-189.
    12. Maximilian Vermorken & Ariane Szafarz & Hugues Pirotte, 2008. "Sector classification through non-Gaussian similarity," Working Papers CEB 08-032.RS, ULB -- Universite Libre de Bruxelles.
    13. Marc S. Paolella, 2016. "Stable-GARCH Models for Financial Returns: Fast Estimation and Tests for Stability," Econometrics, MDPI, vol. 4(2), pages 1-28, May.
    14. Trung K. Do, 2021. "Socially responsible investing portfolio: An almost stochastic dominance approach," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(1), pages 1122-1132, January.
    15. Herrmann Klaus & Fischer Matthias, 2010. "An Alternative Maximum Entropy Model for Time-Varying Moments with Application to Financial Returns," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(3), pages 1-23, May.
    16. repec:csg:ajrcwp:01 is not listed on IDEAS
    17. Broda, Simon & Paolella, Marc S., 2007. "Saddlepoint approximations for the doubly noncentral t distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2907-2918, March.
    18. Fang, Ying & Li, Qi & Wu, Ximing & Zhang, Daiqiang, 2015. "A data-driven smooth test of symmetry," Journal of Econometrics, Elsevier, vol. 188(2), pages 490-501.
    19. Stavros Stavroyiannis & Leonidas Zarangas, 2013. "Out of Sample Value-at-Risk and Backtesting with the Standardized Pearson Type-IV Skewed Distribution," Panoeconomicus, Savez ekonomista Vojvodine, Novi Sad, Serbia, vol. 60(2), pages 231-247, April.
    20. Luke Hartigan, 2016. "Testing for Symmetry in Weakly Dependent Time Series," Discussion Papers 2016-18, School of Economics, The University of New South Wales.
    21. repec:wyi:journl:002099 is not listed on IDEAS
    22. Zacharias Psaradakis & Marián Vávra, 2015. "A Quantile-based Test for Symmetry of Weakly Dependent Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(4), pages 587-598, July.

    More about this item

    Keywords

    quasi-linear mean; robustness; influence function; breakdown point; Laspeyres index; Paasche index; Fisher index;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:zbw:faucse:882010. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/vierlde.html .

    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.