Limit behavior of the empirical influence function of the median
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.
Year of publication: |
1998
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Authors: | Croux, Christophe |
Published in: |
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 37.1998, 4, p. 331-340
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Publisher: |
Elsevier |
Keywords: | Breakdown point Influence function Location estimator Robustness Sensitivity |
Saved in:
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