Finding the principal points of a random variable

Emilio Carrizosa; E. Conde; A. Castaño; D. Romero–Morales

RAIRO - Operations Research (2010)

  • 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 35.3 (2010): 315-328. <http://eudml.org/doc/197828>.

@article{Carrizosa2010,
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. },
author = {Carrizosa, Emilio, Conde, E., Castaño, A., Romero–Morales, D.},
journal = {RAIRO - Operations Research},
keywords = {Principal points; d.c. functions; branch and bound.; principal points; branch and bound},
language = {eng},
month = {3},
number = {3},
pages = {315-328},
publisher = {EDP Sciences},
title = {Finding the principal points of a random variable},
url = {http://eudml.org/doc/197828},
volume = {35},
year = {2010},
}

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
DA - 2010/3//
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.; principal points; branch and bound
UR - http://eudml.org/doc/197828
ER -

References

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  1. E. Carrizosa, E. Conde, A. Casta no, I. Espinosa, I. González and D. Romero-Morales, Puntos principales: Un problema de Optimización Global en Estadística, Presented at XXII Congreso Nacional de Estadística e Investigación Operativa. Sevilla (1995).  
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  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. T. Tarpey, Two principal points of symmetric, strongly unimodal distributions. Statist. Probab. Lett.20 (1994) 253-257.  
  14. T. Tarpey, Principal points and self-consistent points of symmetric multivariate distributions. J. Multivariate Anal.53 (1995) 39-51.  
  15. T. Tarpey, L. Li and B. Flury, Principal points and self-consistent points of elliptical distributions. Ann. Statist.23 (1995) 103-112.  
  16. A. Zoppè, Principal points of univariate continuous distributions. Statist. Comput.5 (1995) 127-132.  
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