Davies, P. Laurie; Gather, Ursula Addendum to the discussion of “Breakdown and groups”. (English) Zbl 1113.62063 Ann. Stat. 34, No. 3, 1577-1579 (2006). Summary: In his discussion of our paper, Ann. Statist. 33, No. 3, 977–1035 (2005; Zbl 1077.62041)], D. E. Tyler pointed out that the theory developed there could not be applied to the case of directional data. He related the breakdown of directional functionals to the problem of definability. In this addendum we provide a concept of breakdown defined in terms of definability and not in terms of bias. If a group of finite order \(k\) acts on the sample space we show that the breakdown point can be bounded above by \((k-1)/k\). In the case of directional data there is a group of order \(k=2\) giving an upper bound of \(1/2\). Cited in 5 Documents MSC: 62H11 Directional data; spatial statistics 62G35 Nonparametric robustness Keywords:breakdown; equivariance; directional data Citations:Zbl 1077.62041 × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Davies, P. L. and Gather, U. (2005). Breakdown and groups (with discussion). Ann. Statist. 33 977–1035. · Zbl 1077.62041 · doi:10.1214/009053604000001138 [2] He, X. and Simpson, D. G. (1992). Robust direction estimation. Ann. Statist. 20 351–369. · Zbl 0761.62035 · doi:10.1214/aos/1176348526 [3] Ko, D. and Guttorp, P. M. (1988). Robustness of estimators for directional data. Ann. Statist. 16 609–618. · Zbl 0645.62045 · doi:10.1214/aos/1176350822 [4] Mardia, K. V. (1972). Statistics of Directional Data . Academic Press, London. · Zbl 0244.62005 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.