ASYMPTOTICS OF THE REPEATED MEDIAN SLOPE ESTIMATOR

• 成果类型: Article
• 署名作者: HOSSJER, O; ROUSSEEUW, PJ; CROUX, C
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325638
• 发表日期: 1994
• 页码: 1478-1501
• 关键词: regression

摘要

The influence function is determined for (twice) repeated median estimators with arbitrary kernel functions, and more generally in the case where the two medians are replaced by a general class of estimators. Asymptotic normality is then established for the repeated median estimator of the slope parameter in simple linear regression. In this case the influence function is hounded. For bivariate Gaussian data the efficiency becomes 4/pi(2) approximate to 40.5%, which is the square of the efficiency of the univariate median. The asymptotic results are compared with finite-sample efficiencies. It turns out that the convergence to the asymptotic behavior is extremely slow.