MULTIVARIATE LOCATION ESTIMATION USING EXTENSION OF R-ESTIMATES THROUGH U-STATISTICS TYPE APPROACH

• 成果类型: Article
• 署名作者: CHAUDHURI, P
• 署名单位: University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348662
• 发表日期: 1992
• 页码: 897-916
• 关键词: sign test; matrices; version

摘要

We consider a class of U-statistics type estimates for multivariate location. The estimates extend some R-estimates to multivariate data. In particular, the class of estimates includes the multivariate median considered by Gini and Galvani (1929) and Haldane (1948) and a multivariate extension of the well-known Hodges-Lehmann (1963) estimate. We explore large sample behavior of these estimates by deriving a Bahadur type representation for them. In the process of developing these asymptotic results, we observe some interesting phenomena that closely resemble the famous shrinkage phenomenon observed by Stein (1956) in high dimensions. Interestingly, the phenomena that we observe here occur even in dimension d = 2.