Weighted halfspace depth

Daniel Hlubinka; Lukáš Kotík; Ondřej Vencálek

Kybernetika (2010)

  • Volume: 46, Issue: 1, page 125-148
  • ISSN: 0023-5954

Abstract

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Generalised halfspace depth function is proposed. Basic properties of this depth function including the strong consistency are studied. We show, on several examples that our depth function may be considered to be more appropriate for nonsymetric distributions or for mixtures of distributions.

How to cite

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Hlubinka, Daniel, Kotík, Lukáš, and Vencálek, Ondřej. "Weighted halfspace depth." Kybernetika 46.1 (2010): 125-148. <http://eudml.org/doc/37708>.

@article{Hlubinka2010,
abstract = {Generalised halfspace depth function is proposed. Basic properties of this depth function including the strong consistency are studied. We show, on several examples that our depth function may be considered to be more appropriate for nonsymetric distributions or for mixtures of distributions.},
author = {Hlubinka, Daniel, Kotík, Lukáš, Vencálek, Ondřej},
journal = {Kybernetika},
keywords = {data depth; nonparametric multivariate analysis; strong consistency of depth; mixture of distributions; data depth; nonparametric multivariate analysis; strong consistency of depth; mixture of distributions},
language = {eng},
number = {1},
pages = {125-148},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Weighted halfspace depth},
url = {http://eudml.org/doc/37708},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Hlubinka, Daniel
AU - Kotík, Lukáš
AU - Vencálek, Ondřej
TI - Weighted halfspace depth
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 1
SP - 125
EP - 148
AB - Generalised halfspace depth function is proposed. Basic properties of this depth function including the strong consistency are studied. We show, on several examples that our depth function may be considered to be more appropriate for nonsymetric distributions or for mixtures of distributions.
LA - eng
KW - data depth; nonparametric multivariate analysis; strong consistency of depth; mixture of distributions; data depth; nonparametric multivariate analysis; strong consistency of depth; mixture of distributions
UR - http://eudml.org/doc/37708
ER -

References

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  2. Breakdown properties of location estimates based on halfspace depth and projected outlyingness, Ann. Statist. 20 (1992), 1803–1827. MR1193313
  3. On a notion of data depth based on random simplices, Ann. Statist. 18 (1990), 405–414. Zbl0701.62063MR1041400
  4. DIMACS; Data Depth: Robust Multivariate Analysis, Computational Geometry and Applications, American Mathematical Society, Providence RI 2006. MR2343124
  5. Computing the center of planar point sets, In: DIMACS; Discrete and Computational Geometry (J. E. Goodman, R. Pollack, and W. Steiger, eds.). American Mathematical Society, 1992. MR1143299
  6. On depth and deep points: a calculus, Ann. Statist. 30 (2002), 1681–1736. Zbl1039.62046MR1969447
  7. Algorithm AS307: bivariate location depth, J. Roy. Statist. Soc.-C 45 (1996), 516–526. 
  8. Mathematics and picturing data, In: Proc. 1975 International Congress of Mathematics, Vol. 2 (1975), pp. 523–531. MR0426989
  9. Empirical Processes and M-Estimates, Cambridge, 2000. 
  10. General notion of statistical depth function, Ann. Statist. 28 (2000), 461–482. MR1790005
  11. Structural properties and convergence results for contours of sample statistical depth functions, Ann. Statist. 28 (2000), 483–499. MR1790006

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