Comptes Rendus
no. 3-4
Statistics
Asymptotic properties of a dimension-robust quadratic dependence measure

Presented by: Paul Deheuvels

Sophie Achard1
1 Brain Mapping Unit, University of Cambridge, Downing Site, Cambridge CB2 3EB, UK
Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 213-216.

The quadratic dependence measure is related to measures used in independence tests, but is derivable, thus suitable for independent component analysis. An adjustable kernel allows to accelerate the convergence of the estimator without affecting the bias.

La mesure de dépendance quadratique peut-être reliée aux mesures utilisées dans les tests d'indépendance, mais étant de plus dérivable, on peut l'utiliser dans les méthodes d'analyse en composantes indépendantes. Un noyau ajustable permet d'accélérer la convergence de l'estimateur sans pour autant affecter son biais.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.10.043

Sophie Achard 1

1 Brain Mapping Unit, University of Cambridge, Downing Site, Cambridge CB2 3EB, UK 
@article{CRMATH_2008__346_3-4_213_0,
     author = {Sophie Achard},
     title = {Asymptotic properties of a dimension-robust quadratic dependence measure},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {213--216},
     publisher = {Elsevier},
     volume = {346},
     number = {3-4},
     year = {2008},
     doi = {10.1016/j.crma.2007.10.043},
     language = {en},
}
TY  - JOUR
AU  - Sophie Achard
TI  - Asymptotic properties of a dimension-robust quadratic dependence measure
JO  - Comptes Rendus. Mathématique
PY  - 2008
SP  - 213
EP  - 216
VL  - 346
IS  - 3-4
PB  - Elsevier
DO  - 10.1016/j.crma.2007.10.043
LA  - en
ID  - CRMATH_2008__346_3-4_213_0
ER  - 
%0 Journal Article
%A Sophie Achard
%T Asymptotic properties of a dimension-robust quadratic dependence measure
%J Comptes Rendus. Mathématique
%D 2008
%P 213-216
%V 346
%N 3-4
%I Elsevier
%R 10.1016/j.crma.2007.10.043
%G en
%F CRMATH_2008__346_3-4_213_0
Sophie Achard. Asymptotic properties of a dimension-robust quadratic dependence measure. Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 213-216. doi : 10.1016/j.crma.2007.10.043. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.10.043/

[1] S. Achard, D.T. Pham, C. Jutten, Quadratic dependence measure for non linear blind sources separation, in: Proc. Int. Workshop ICA2003, April 2003, pp. 263–268

[2] J.R. Blum; J. Kiefer; M. Rosenblatt Distribution free tests of independence based on the sample distribution functions, Ann. Math. Stat., Volume 32 (1961), pp. 485-498

[3] A. Chen; P.J. Bickel Consistent independent component analysis and prewhitening, IEEE Trans. Signal Processing, Volume 53 (2005) no. 10, pp. 3625-3632

[4] S. Csörgő Limit behaviour of the empirical characteristic function, Ann. Probab., Volume 9 (1981) no. 1, pp. 130-144

[5] J. Eriksson; V. Koivunen Characteristic function based independent component analysis, Signal Processing, Volume 83 (2003), pp. 2195-2208

[6] A. Feuerverger A consistent test for bivariate dependence, Int. Statist. Rev., Volume 61 (1993) no. 3, pp. 419-433

[7] W. Hoeffding A class of statistics with asymptotically normal distribution, Ann. Math. Stat., Volume 19 (1948), pp. 293-325

[8] W. Hoeffding A non-parametric test of independence, Ann. Math. Stat., Volume 19 (1948), pp. 546-557

[9] A. Kankainen, Consistent testing of total independence based on empirical characteristic functions, PhD thesis, University of Jyväskylä, 1995

[10] M. Rosenblatt A quadratic measure of deviation of two-dimensional density estimates and a test of independence, Ann. Statist., Volume 3 (1975) no. 1, pp. 1-14

Cited by Sources:

Comments - Policy