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Asymptotic distributions of the maximal depth estimators for regression and multivariate location. (English) Zbl 1007.62009

Summary: We derive the asymptotic distribution of the maximal depth regression estimator proposed by P.J. Rousseeuw and M. Hubert [J. Am. Stat. Assoc. 94, No. 446, 388-433 (1999; this Zbl 1007.62060)]. 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.

MSC:

62E20 Asymptotic distribution theory in statistics
62J05 Linear regression; mixed models
62H12 Estimation in multivariate analysis

Citations:

Zbl 1007.62060
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References:

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