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Finding the principal points of a random variable

Published online by Cambridge University Press:  15 August 2002

Emilio Carrizosa ,
E. Conde ,
A. Castaño  and
D. Romero–Morales
Emilio Carrizosa
Affiliation:
Facultad de Matemáticas, Universidad de Sevilla, C/ Tarfia s/n, 41012 Sevilla, Spain.
E. Conde
Affiliation:
Facultad de Matemáticas, Universidad de Sevilla, C/ Tarfia s/n, 41012 Sevilla, Spain.
A. Castaño
Affiliation:
Departamento de Matemáticas, E.U. Empresariales, Universidad de Cádiz, C/ Por Vera, N. 54, Jerez de la Frontera, Cádiz, Spain.
D. Romero–Morales
Affiliation:
Facultad de Matemáticas, Universidad de Sevilla, C/ Tarfia s/n, 41012 Sevilla, Spain. Faculty of Economics and Business Administration, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands.
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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.

Keywords

Principal pointsd.c. functionsbranch and bound.
Type
Research Article
Information
RAIRO - Operations Research , Volume 35 , Issue 3 , July 2001 , pp. 315 - 328
Copyright
© EDP Sciences, 2001

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References

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