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A note on Tyler’s modification of the MAD for the Stahel-Donoho estimator. (English) Zbl 0881.62033

Summary: D. E. Tyler [ibid. 22, No. 2, 1024-1044 (1994; Zbl 0815.62015)] proposed a modification of the MAD in order to achieve the maximal possible finite sample breakdown point for the Stahel-Donoho estimator based upon the median and the modified MAD. A proof is not given, however, and as far as we know has not been published yet. Moreover there seems to be an error concerning the exact definition of the modified MAD which is needed to achieve this goal.
For the sake of theoretical completeness and in order to correct this error we calculate the finite sample breakdown point of modifications of the MAD and point out which of these modifications lead to a Stahel-Donoho estimator with maximal finite sample breakdown point.

MSC:

62F35 Robustness and adaptive procedures (parametric inference)
62H12 Estimation in multivariate analysis

Citations:

Zbl 0815.62015
Full Text: DOI