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2014

Fast computation of Tukey trimmed regions and median in dimension $p>2$

Liu, Xiaohui, Mosler, Karl, Mozharovskyi, Pavlo

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Given data in $\mathbb{R}^{p}$, a Tukey $\kappa$-trimmed region is the set of all points that have at least Tukey depth $\kappa$ w.r.t.

the data.
As they are visual, affine equivariant and robust, Tukey regions are useful tools in nonparametric multivariate analysis.
While these regions are easily defined and interpreted, their practical use in applications has been impeded so far by the lack of efficient computational procedures in dimension $p > 2$.

Fast computation of Tukey trimmed regions and median in dimension $p>2$ · Around

Built on

Tukey, J. W
1975
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Reaven, G. M. and Miller, R. G
1979
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Donoho, D. L
1982
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Rousseeuw, P. J. and Leroy, A. M
1987
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Barber, C. B., Dobkin, D. P., and Huhdanpaa, H
1996
Earlier work this paper cites.
Ruts, I. and Rousseeuw, P. J
1996
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Yeh, A. B. and Singh, K
1997
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Rousseeuw, P. J. and Ruts, I
1998
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Rousseeuw, P. J. and Struyf, A
1998
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Azzalini, A. and Capitanio, A
1999
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Liu, R. Y., Parelius, J. M., Singh, K
1999
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Rousseeuw, P. J., Ruts, I., and Tukey, J. W
1999
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