Finding the principal points of a random variable

Emilio Carrizosa; E. Conde; A. Castaño[1]; D. Romero-Morales[2]

  • [1] Departamento de Matemáticas, E.U. Empresariales, Universidad de Cádiz, C/ Por Vera, N. 54, Jerez de la Frontera, Cádiz, Spain.
  • [2] Faculty of Economics and Business Administration, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands.

RAIRO - Operations Research - Recherche Opérationnelle (2001)

  • Volume: 35, Issue: 3, page 315-328
  • ISSN: 0399-0559

Abstract

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The p -principal points of a random variable X with finite second moment are those p points in ℝ minimizing the expected squared distance from X to the closest point. Although the determination of principal points involves in general the resolution of a multiextremal optimization problem, existing procedures in the literature provide just a local optimum. In this paper we show that standard Global Optimization techniques can be applied.

How to cite

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Carrizosa, Emilio, et al. "Finding the principal points of a random variable." RAIRO - Operations Research - Recherche Opérationnelle 35.3 (2001): 315-328. <http://eudml.org/doc/105249>.

@article{Carrizosa2001,
abstract = {The $p$-principal points of a random variable $X$ with finite second moment are those $p$ points in $\mathbb \{R\}$ minimizing the expected squared distance from $X$ to the closest point. Although the determination of principal points involves in general the resolution of a multiextremal optimization problem, existing procedures in the literature provide just a local optimum. In this paper we show that standard Global Optimization techniques can be applied.},
affiliation = {Departamento de Matemáticas, E.U. Empresariales, Universidad de Cádiz, C/ Por Vera, N. 54, Jerez de la Frontera, Cádiz, Spain.; Faculty of Economics and Business Administration, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands.},
author = {Carrizosa, Emilio, Conde, E., Castaño, A., Romero-Morales, D.},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {principal points; d.c. functions; branch and bound},
language = {eng},
number = {3},
pages = {315-328},
publisher = {EDP-Sciences},
title = {Finding the principal points of a random variable},
url = {http://eudml.org/doc/105249},
volume = {35},
year = {2001},
}

TY - JOUR
AU - Carrizosa, Emilio
AU - Conde, E.
AU - Castaño, A.
AU - Romero-Morales, D.
TI - Finding the principal points of a random variable
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 2001
PB - EDP-Sciences
VL - 35
IS - 3
SP - 315
EP - 328
AB - The $p$-principal points of a random variable $X$ with finite second moment are those $p$ points in $\mathbb {R}$ minimizing the expected squared distance from $X$ to the closest point. Although the determination of principal points involves in general the resolution of a multiextremal optimization problem, existing procedures in the literature provide just a local optimum. In this paper we show that standard Global Optimization techniques can be applied.
LA - eng
KW - principal points; d.c. functions; branch and bound
UR - http://eudml.org/doc/105249
ER -

References

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  12. [12] S. Rowe, An Algorithm for Computing Principal Points with Respect to a Loss Function in the Unidimensional Case. Statist. Comput. 6 (1997) 187-190. 
  13. [13] T. Tarpey, Two principal points of symmetric, strongly unimodal distributions. Statist. Probab. Lett. 20 (1994) 253-257. Zbl0799.62019MR1294603
  14. [14] T. Tarpey, Principal points and self-consistent points of symmetric multivariate distributions. J. Multivariate Anal. 53 (1995) 39-51. Zbl0820.62047MR1333126
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  17. [17] A. Zoppè, On Uniqueness and Symmetry of self-consistent points of univariate continuous distribution. J. Classification 14 (1997) 147-158. Zbl0891.62005MR1449745

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