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ST ] 2 3 A ug 2 01 9 Regression medians and uniqueness
| Content Provider | Semantic Scholar |
|---|---|
| Author | Zuo, Yijun |
| Copyright Year | 2019 |
| Abstract | Notion of median in one dimension is a foundational element in nonparametric statistics. It has been extended to multi-dimensional cases both in location and in regression via notions of data depth. Regression depth (RD) and projection regression depth (PRD) represent the two most promising notions in regression. Carrizosa depth DC is another depth notion in regression. Depth induced regression medians (maximum depth estimators) serve as robust alternatives to the classical least squares estimator. The uniqueness of regression medians is indispensable in the discussion of the asymptotics (consistency and limiting distribution) of sample regression medians. Are the regression medians induced from RD, PRD, and DC unique? Answering this question is the main goal of this article. It is found that only the regression median induced from PRD possesses the uniqueness property. This and other findings indicate that the PRD and its induced median are highly favorable among its leading competitors. AMS 2000 Classification: Primary 62G08, 62G35; Secondary 62J05, 62J99. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv-export-lb.library.cornell.edu/pdf/1906.10461 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
