A robust scale estimator based on the shortest half

Peter Rousseeuw and A.M. Leroy

Statistica Neerlandica, 1988, vol. 42, issue 2, 103-116

Abstract: A new robust estimator of scale is considered, which is proportional to the length of the shortest half of the sample. The estimator is compared to the interquartile range and the median absolute deviation, that are also based on order statistics. All three estimators have the same influence function, but their breakdown points differ. It also turns out that one needs a finite‐sample correction factor which depends on mod(sample size, 4) to achieve approximate unbiasedness at normal distributions.

Date: 1988
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