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A class of high-breakdown scale estimators based on subranges. (English) Zbl 0774.62035
Summary: We consider a new class of scale estimators with 50% breakdown point. The estimators are defined as order statistics of certain subranges. They all have a finite-sample breakdown point of \([n/2]/n\), which is the best possible value. (Here, \([\dots]\) denotes the integer part.) One estimator in this class has the same influence function as the median absolute deviation and the least median of squares (LMS) scale estimator (i.e., the length of the shortest half), but its finite-sample efficiency is higher.
If we consider the standard deviation of a subsample instead of its range, we obtain a different class of 50% breakdown estimators. This class contains the least trimmed squares (LTS) scale estimator. Simulation shows that the LTS scale estimator is nearly unbiased, so it does not need a small-sample correction factor. Surprisingly, the efficiency of the LTS scale estimator is less than that of the LMS scale estimator.

62F35 Robustness and adaptive procedures (parametric inference)
62F10 Point estimation
Full Text: DOI
[1] DOI: 10.1214/aos/1176343648 · Zbl 0351.62031
[2] Donoho D. L., A Festschrift for Erich Lehmann (1983)
[3] DOI: 10.2307/2285666 · Zbl 0305.62031
[4] Hampel F. R., Robust Statistics: the Approach based on Influence Functions (1986) · Zbl 0593.62027
[5] Johnson N. L., Continuous Univariate Distributions-I (1970)
[6] Rousseeuw P. J., The IMS Bulletin 12 pp 155– (1983)
[7] DOI: 10.2307/2288718 · Zbl 0547.62046
[8] DOI: 10.1002/0471725382
[9] DOI: 10.1111/j.1467-9574.1988.tb01224.x · Zbl 0652.62032
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