Dimensionless measures of variability and dependence for multivariate continuous distributions

Communications in Statistics - Theory and Methods

Volumn 36, Issue 10, 2007, Pages 1845-1854

  Peña, Daniel ^a   Van Der Linde, Angelika ^b  

^a UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^b UNIVERSITY OF BREMEN   (Germany)

Author keywords

Entropy; Independent components; Mutual information

Indexed keywords

COVARIANCE MATRIX; ENTROPY; INDEPENDENT COMPONENT ANALYSIS; RANDOM VARIABLES; VECTORS;

INDEPENDENT COMPONENTS; MUTUAL INFORMATION;

MULTIVARIANT ANALYSIS;

EID: 34547345252     PISSN: 03610926     EISSN: 1532415X     Source Type: Journal    
DOI: 10.1080/03610920601126449     Document Type: Article

References (19)

1. Beirlant, J., Dudewicz, E. J., Gyöfi, L., van der Meulen, E. C. (1997). Nonparametric entropy estimation: an overview. Int. J. Mathemat. Statist. Sc. 6:17-39.
2. Berg, A., Meyer, R., Yu, J. (2004). Deviance information criterion for comparing stochastic volatility models. J. Bus. Econ. Statist. 22:107-120.
3. Cover, T. M., Thomas, J. A. (1991). Information Theory. New York: Wiley.
4. Darbellay, G. A. (1998). Predictability: an information-theoretic perspective. In: Prochäka, A. et al., eds. Signal Analysis and Prediction. Boston: Birkháser, pp. 249-262.
5. Darbellay, G. A. (1999). An estimator of the mutual information based on a criterion for independence. Computat. Statist. Data Anal. 32:1-17.
6. Darbellay, G. A., Vajda, I. (1999). Estimation of the information by an adaptive partitioning of the observation space. IEEE Trans. Information Theor. 45:1315-1321.
7. Darbellay, G. A., Vajda, I. (2000). Entropy expressions for multivariate continuous distributions. IEEE Trans. Information Theor. 46:709-712.
8. Guerrero-Cusumano, J.-L. (1996a). An asymptotic test of independence for multivariate t and cauchy random variables with applications. Information Sc. 92:33-45.
9. Guerrero-Cusumano, J.-L. (1996b). A measure of total variability for the multivariate t distribution with applications to finance. Information Sc. 92:47-63.
10. Guerrero-Cusumano, J.-L. (1998). Measures of dependence for the multivariate t distribution with applications to the stock market. Commun. Statist. Theor. Meth. 27:2985-3006.
11. Hyväinen, A., Karhunen, J., Oja, E. (2001). Independent Component Analysis. New York: Wiley.
12. Joe, H. (1989a). Relative entropy measures of multivariate dependence. J. Amer. Statist. Assoc. 84:157-164.
13. Joe, H. (1989b). Estimation of entropy and other functionals of a multivariate density. Ann. Instit. Statist. Math. 41:683-697.
14. Kapur, J. N., Dhande, M. (1986). On the entropic measures of stochastic dependence. Indian J. Pure Appl. Math. 17:581-595.
15. Peña, D., Rodríguez, J. (2003). Descriptive measures of multivariate scatter and linear dependence. J. Multivariate Anal. 58:361-374.
16. Roberts, S., Everson, R. Eds. (2001). Independent Component Analysis: Principles and Practice. Cambridge: Cambridge University Press.
17. Shannon, C. E. (1948). A mathematical theory of communication. Bell Syst. Technical J. 27:379-423, 623-656.
18. Theil, H., Chung, C.-F. (1988). Information-theoretic measures of fit for univariate and multivariate linear regressions. Amer. Statistician 42:249-252.
19. Vasicek, O. (1976). A test for normality based on sample entropy. J. Roy. Statist. Soc. B 38:54-59.