Finding the principal points of a random variable

Issue		RAIRO Oper. Res. Volume 35, Number 3, July-September 2001


Page(s)		315 - 328
DOI		10.1051/ro:2001117

DOI: 10.1051/ro:2001117

RAIRO Oper. Res. 35 (2001) 315-328

Finding the principal points of a random variable

Emilio Carrizosa¹, E. Conde¹, A. Castaño² and D. Romero-Morales^{3, 1}

¹ Facultad de Matemáticas, Universidad de Sevilla, C/ Tarfia s/n, 41012 Sevilla, Spain.
² Departamento de Matemáticas, E.U. Empresariales, Universidad de Cádiz, C/ Por Vera, N. 54, Jerez de la Frontera, Cádiz, Spain.
³ Faculty of Economics and Business Administration, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands.

(Received December, 1999. Accepted April, 2001)

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.

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