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location depth 1 multivariate ranking 1 reconstruction algorithm 1 regression depth 1
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Rousseeuw, Peter J. 1 Struyf, Anja J. 1
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Journal of Multivariate Analysis 1
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Halfspace Depth and Regression Depth Characterize the Empirical Distribution
Struyf, Anja J.; Rousseeuw, Peter J. - In: Journal of Multivariate Analysis 69 (1999) 1, pp. 135-153
For multivariate data, the halfspace depth function can be seen as a natural and affine equivariant generalization of the univariate empirical cdf. For any multivariate data set, we show that the resulting halfspace depth function completely determines the empirical distribution. We do this by...
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