# 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

## Access Full Article

top## Abstract

top## How to cite

topCarrizosa, 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

top- 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).
- D.R. Cox, A use of complex probabilities in the theory of stochastic processes, in Proc. of the Cambridge Philosophical Society, Vol. 51 (1955) 313-319. Zbl0066.37703
- B. Flury, Principal points. Biometrika77 (1990) 33-41. Zbl0691.62053
- B. Flury and T. Tarpey, Representing a Large Collection of Curves: A Case for Principal Points. Amer. Statist.47 (1993) 304-306.
- R. Fourer, D.M. Gay and B.W. Kernigham, AMPL, A modeling language for Mathematical Programming. The Scientific Press, San Francisco (1993).
- E. Gelenbe and R.R. Muntz, Probabilistic Models of Computer Systems-Part I. Acta Inform.7 (1976) 35-60. Zbl0343.60066
- R. Horst, An Algorithm for Nonconvex Programming Problems. Math. Programming10 (1976) 312-321. Zbl0337.90062
- R. Horst and H. Tuy, Global Optimization. Deterministic Approaches. Springer-Verlag, Berlin (1993). Zbl0704.90057
- S.P. Lloyd, Least Squares Quantization in PCM. IEEE Trans. Inform. Theory 28 (1982) 129-137. Zbl0504.94015
- L. Li and B. Flury, Uniqueness of principal points for univariate distributions. Statist. Probab. Lett.25 (1995) 323-327. Zbl0837.62017
- K. Pötzelberger and K. Felsenstein, An asymptotic result on principal points for univariate distribution. Optimization28 (1994) 397-406. Zbl0813.62012
- S. Rowe, An Algorithm for Computing Principal Points with Respect to a Loss Function in the Unidimensional Case. Statist. Comput.6 (1997) 187-190.
- T. Tarpey, Two principal points of symmetric, strongly unimodal distributions. Statist. Probab. Lett.20 (1994) 253-257. Zbl0799.62019
- T. Tarpey, Principal points and self-consistent points of symmetric multivariate distributions. J. Multivariate Anal.53 (1995) 39-51. Zbl0820.62047
- T. Tarpey, L. Li and B. Flury, Principal points and self-consistent points of elliptical distributions. Ann. Statist.23 (1995) 103-112. Zbl0822.62042
- A. Zoppè, Principal points of univariate continuous distributions. Statist. Comput.5 (1995) 127-132.
- A. Zoppè, On Uniqueness and Symmetry of self-consistent points of univariate continuous distribution. J. Classification14 (1997) 147-158. Zbl0891.62005

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.