2004/08/01 by Matias Salibian-Barrera, Ruben H. Zamar
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Risk and Portfolio Optimization #Statistical Methods and Inference #math.ST #msc:62E20. #msc:62F12 #msc:62F35 #stat.TH
paper · pdf · doi:10.1214/009053604000000544
published as Annals of Statistics 2004, Vol. 32, No. 4, 1434-1447 · Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/009053604000000544
openalex publication_date 2004/08/01 · arxiv created 2004/10/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Most asymptotic results for robust estimates rely on regularity conditions that are difficult to verify in practice. Moreover, these results apply to fixed distribution functions. In the robustness context the distribution of the data remains largely unspecified and hence results that hold uniformly over a set of possible distribution functions are of theoretical and practical interest. Also, it is desirable to be able to determine the size of the set of distribution functions where the uniform properties hold. In this paper we study the problem of obtaining verifiable regularity conditions that suffice to yield uniform consistency and uniform asymptotic normality for location robust estimates when the scale of the errors is unknown. We study M-location estimates calculated with an S-scale and we obtain uniform asymptotic results over contamination neighborhoods. Moreover, we show how to calculate the maximum size of the contamination neighborhoods where these uniform results hold. There is a trade-off between the size of these neighborhoods and the breakdown point of the scale estimate.