Uniform asymptotics for robust location estimates when the scale is unknown

• 成果类型: Article
• 署名作者: Salibian-Barrera, M; Zamar, RH
• 署名单位: Carleton University; University of British Columbia
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000000544
• 发表日期: 2004
• 页码: 1434-1447
• 关键词: FUNCTIONALS; regression; parameters; variances; MODEL

摘要

Most asymptotic results for robust estimates rely on regularity conditions that are difficult to verily 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.