Regularity and uniqueness for constrained M-estimates and redescending M-estimates

• 成果类型: Article
• 署名作者: Kent, JT; Tyler, DE
• 署名单位: University of Leeds; Rutgers University System; Rutgers University New Brunswick
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/996986508
• 发表日期: 2001
• 页码: 252-265
• 关键词: multivariate location

摘要

Constrained M-estimates of multivariate location and scatter are found by finding the global minimum of an objective function subject to a constraint. They are related to redescending M-estimates of multivariate location and scatter since any stationary point of the objective function corresponds to such an M-estimate. Unfortunately, even for the population form of the estimator, that is, the constrained dl-functional, the objective function may have multiple stationary points. In this paper, we give conditions under which the objective function is as well behaved as possible, in particular that it has at most one local minimum. To carry out this task, we introduce a class of distributions which we call regular distributions with respect to a particular objective function.