# Approximate computation of projection depths

@article{Dyckerhoff2020ApproximateCO,
title={Approximate computation of projection depths},
author={Rainer Dyckerhoff and Pavlo Mozharovskyi and Stanislav Nagy},
journal={Comput. Stat. Data Anal.},
year={2020},
volume={157},
pages={107166}
}
• Published 15 July 2020
• Geology
• Comput. Stat. Data Anal.
8 Citations

## Figures and Tables from this paper

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## References

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Summary:Data depth is a concept that measures the centrality of a point in a given data cloud x1, x2,...,xn ∈ ℝ or in a multivariate distribution PX on ℝdd. Every depth defines a family of so–called
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An exact algorithm to compute the location depth in three dimensions in O(n2logn) time and an approximate algorithm that computes the depth of a regression fit in O3+mpn+mnlogn time are constructed.
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Comput. Stat. Data Anal.
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• Mathematics
Electronic Journal of Statistics
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The computational complexity of some depths that satisfy the projection property, such as the halfspace depth or the projection depth, is known to be high, especially for data of higher
In 1975 John Tukey proposed a multivariate median which is th e ‘deepest’ point in a given data cloud inRd (Tukey, 1975). In measuring the depth of an arbitrary point z with respect to the data,
• Mathematics
Comput. Stat. Data Anal.
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• Mathematics
Stat. Comput.
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An exact algorithm is proposed from the view of cutting a convex polytope with hyperplanes to compute the projection depth and most of its associated estimators of dimension p≥2, including Stahel-Donoho location and scatter estimators, projection trimmed mean, projection depth contours and median, etc.
• Mathematics
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The $${ DD}\alpha$$DDα-classifier, a nonparametric fast and very robust procedure, is described and applied to fifty classification problems regarding a broad spectrum of real-world data. The
For a distribution F on R p and a point x in R p , the simplicial depth D(x) is introduced, which is the probability that the point x is contained inside a random simplex whose vertices are p+1