Simultaneous estimation of location parameters for sign-invariant distributions

• 成果类型: Article
• 署名作者: Xu, JL
• 署名单位: University of Houston System; University of Houston
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1069362397
• 发表日期: 1997
• 页码: 2259-2272
• 关键词: spherically symmetric distributions; QUADRATIC LOSS; Minimax Estimation

摘要

Estimation of p, p greater than or equal to 3, location parameters of a distribution of a p-dimensional random vector X is considered under quadratic loss. Explicit estimators which are better than the best invariant one are given for a sign-invariantly distributed random vector X. The results depend only on the second and the third moments of parallel to X-theta parallel to. The generalizations to concave loss functions and to n observations are also considered. Additionally, if the scale is unknown, we investigate the estimators of the location parameters when the observation contains a residual vector.