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|Title:||Asymptotic distributions of the maximal depth estimators for regression and multivariate location||Authors:||Bai, Z.-D.
|Issue Date:||Oct-1999||Citation:||Bai, Z.-D.,He, X. (1999-10). Asymptotic distributions of the maximal depth estimators for regression and multivariate location. Annals of Statistics 27 (5) : 1616-1637. ScholarBank@NUS Repository.||Abstract:||We derive the asymptotic distribution of the maximal depth regression estimator recently proposed in Rousseeuw and Hubert. The estimator is obtained by maximizing a projection-based depth and the limiting distribution is characterized through a max - min operation of a continuous process. The same techniques can be used to obtain the limiting distribution of some other depth estimators including Tukey's deepest point based on half-space depth. Results for the special case of two-dimensional problems have been available, but the earlier arguments have relied on some special geometric properties in the low-dimensional space. This paper completes the extension to higher dimensions for both regression and multivariate location models.||Source Title:||Annals of Statistics||URI:||http://scholarbank.nus.edu.sg/handle/10635/105023||ISSN:||00905364|
|Appears in Collections:||Staff Publications|
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