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

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  • 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
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    1. Gamini Premaratne, 2005. "A Test for Symmetry with Leptokurtic Financial Data," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(2), pages 169-187.
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    Keywords

    quasi-linear mean; robustness; influence function; breakdown point; Laspeyres index; Paasche index; Fisher index;

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