Robustness of the half-space median. (English) Zbl 0833.62033
Summary: We extend D. Donoho and M. Gasko’s [Ann. Stat. 20, No. 4, 1803-1827 (1992; Zbl 0776.62031)] results on finite sample breakdown point for the half-space median to any given data set and, as a consequence, we obtain bounds for the limiting breakdown point for general (in particular, nonsymmetric) distributions. Lower and upper bounds for the breakdown point of the half-space median with respect to the half-space metric are also established; in two-dimensional space, they yield the exact breakdown point. The exact ‘gross error neighborhood’ breakdown point for symmetric distributions is also given.
MSC:
| 62F35 | Robustness and adaptive procedures (parametric inference) |
| 62H12 | Estimation in multivariate analysis |
Keywords:
gross error neighborhood breakdown; robustness; finite sample breakdown point; half-space median; bounds; half-space metricCitations:
Zbl 0776.62031References:
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