On the impact of predictor geometry on the performance on high-dimensional ridge-regularized generalized robust regression estimators

• 成果类型: Article
• 署名作者: El Karoui, Noureddine
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0754-9
• 发表日期: 2018
• 页码: 95-175
• 关键词: ASYMPTOTIC-BEHAVIOR; parameters; matrices; limit; RISK; p2/n

摘要

We study ridge-regularized generalized robust regression estimators, i.e. in the situation where p/n tends to a finite non-zero limit. Our study here focuses on the situation where the errors 's are heavy-tailed and 's have an elliptical-like distribution. Our assumptions are quite general and we do not require homoskedasticity of 's for instance. We obtain a characterization of the limit of , as well as several other results, including central limit theorems for the entries of (beta) over cap.