Limit behavior of the empirical influence function of the median

Christophe Croux

Statistics & Probability Letters, 1998, vol. 37, issue 4, 331-340

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.

Keywords: Breakdown; point; Influence; function; Location; estimator; Robustness; Sensitivity (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (3)

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