3Measuring Robustness

In order to measure the effect of different locations of an outlier on an estimate, consider adding to a sample c03-i0001 an extra data point c03-i0002 that is allowed to range on the whole real line. We define the sensitivity curve of the estimator c03-i0003 for the sample c03-i0004 as the difference


as a function of the location c03-i0005 of the outlier.

For purposes of plotting and comparing sensitivity curves across sample sizes, it is convenient to use standardized sensitivity curves, obtained by multiplying (3.1) by c03-i0006 (see also Section 3.1). To make our examples clearer, we use a “sample” formed from standard normal distribution quantiles, instead of a random one. Figure 3.1 plots:

  • the standardized sensitivity curves of the median
  • the 10% trimmed mean
  • the 10% Winsorized mean
  • the Huber M‐estimator with ...

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