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Asymptotics for the Tukey Median

✍ Scribed by Jean-Claude Massé

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
139 KB
Volume
81
Category
Article
ISSN
0047-259X

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✦ Synopsis

The asymptotic distribution of the Tukey median has recently been obtained by Nolan in a bivariate setting and by Bai and He in the general multivariate case. To establish their theorem, these authors made a strong symmetry hypothesis on the distribution and, in the case of Bai and He, assumed the existence of a density function with a gradient satisfying a finite-moment condition. This paper extends the above result by deriving the asymptotic distribution of the above location estimate without making any symmetry or differentiability assumption on the distribution.

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