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Limit behavior of the empirical influence function of the median

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  • Croux, Christophe

Abstract

The empirical influence function EIF(x, Tn; X) measures the influence of an observation x on the estimator Tn at a sample X of size n. In this note we show that the empirical influence function of the median is not a consistent estimator of the corresponding influence function. This observation leads to a reconsideration of the most -robustness property of the median. We will prove and show by simulations that the median is less robust to single outliers than commonly believed.

Suggested Citation

  • Croux, Christophe, 1998. "Limit behavior of the empirical influence function of the median," Statistics & Probability Letters, Elsevier, vol. 37(4), pages 331-340, March.
    • Handle: RePEc:eee:stapro:v:37:y:1998:i:4:p:331-340
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    References listed on IDEAS

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    1. Oosterhoff, J., 1994. "Trimmed mean or sample median?," Statistics & Probability Letters, Elsevier, vol. 20(5), pages 401-409, August.
    2. A. Christmann & U. Gather & G. Scholz, 1994. "Some properties of the length of the shortest half," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 48(3), pages 209-213, November.
    3. Cabrera, J. & Maguluri, G. & Singh, K., 1994. "An odd property of the sample median," Statistics & Probability Letters, Elsevier, vol. 19(4), pages 349-354, March.
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    Cited by:

    1. Qingyang Zhang, 2024. "Asymptotic expected sensitivity function and its applications to measures of monotone association," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(5), pages 877-896, October.
    2. Bar-Hen, Avner & Poggi, Jean-Michel, 2016. "Influence measures and stability for graphical models," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 145-154.
    3. Maria Iannario & Anna Clara Monti & Domenico Piccolo, 2016. "Robustness issues for cub models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 731-750, December.

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