Abstract
We consider the asymptotic behavior, both in distribution and almost sure, of the Bahadur-Kiefer representation of the two dimensional spatial medians. The rates appearing in this expansion are non-standard. The rate in the almost sure expansion is n(2 log n)-1/2(2 log log n)-1. The set of clusters points in the almost sure representation is obtained. The distribution of the Bahadur-Kiefer representation of the two dimensional spatial medians converges with rate n(2 log n)-1/2 to a limit that is determined precisely.
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Arcones, M.A. The Bahadur-Kiefer Representation of the Two Dimensional Spatial Medians. Annals of the Institute of Statistical Mathematics 50, 71–86 (1998). https://doi.org/10.1023/A:1003449330662
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DOI: https://doi.org/10.1023/A:1003449330662