Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-25T17:30:01.859Z Has data issue: false hasContentIssue false
  • English
  • Français

MULTIVARIATE DISPERSION ORDER AND THE NOTION OF COPULA APPLIED TO THE MULTIVARIATE t-DISTRIBUTION

Published online by Cambridge University Press:  22 June 2005

J. P. Arias-Nicolás ,
J. M. Fernández-Ponce ,
P. Luque-Calvo  and
A. Suárez-Llorens
J. P. Arias-Nicolás
Affiliation:
Department of Mathematics, University of Extremadura, Extremadura, Spain, E-mail: jparias@unex.es
J. M. Fernández-Ponce
Affiliation:
Department of Statistics, University of Sevilla, 41013 Sevilla, Spain, E-mail: ferpon@us.es; calvo@us.es
P. Luque-Calvo
Affiliation:
Department of Statistics, University of Sevilla, 41013 Sevilla, Spain, E-mail: ferpon@us.es; calvo@us.es
A. Suárez-Llorens
Affiliation:
Department of Statistics, University of Cádiz, 11002 Cádiz, Spain, E-mail: alfonso.suarez@uca.es
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the concept of multivariate dispersion order, defined as the existence of an expansion function that maps a random vector to another one, for multivariate distributions with the same dependence structure. As a particular case, we can order the multivariate t-distribution family in dispersion sense. Finally, we use these results in the problem of detection and characterization of influential observations in regression analysis. This problem can often be used to compare two multivariate t-distributions.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 19 , Issue 3 , July 2005 , pp. 363 - 375
Copyright
© 2005 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Arellano-Valle, R.B. & Bolfarine, H. (1995). On some characterizations of the t-distribution. Statistics and Probability Letters 25: 79–85.Google Scholar
Bernardo, J.M. & Smith, A.F.M. (1994). Bayesian theory. New York: Wiley.CrossRef
Capéraà, P. (1988). Tail ordering and asymptotic efficiency of rank test. The Annals of Statistics 16(1): 470–478.Google Scholar
Cook, R.D. & Weisberg, S. (1980). Finding influential cases in regression: A review. Technometrics 22: 495–508.Google Scholar
Deshpandé, J.V. & Kochar, S.C. (1983). Dispersive ordering is the same as tail ordering. Advances in Applied Probability 15: 686–687.Google Scholar
Doksum, K. (1969). Starshaped transformations and the power of rank tests. Annals of Mathematical Statistics 40: 1167–1176.Google Scholar
Fernández-Ponce, J.M. & Suárez-Llorens, A. (2003). A multivariate dispersion ordering based on quantiles more widely separated. Journal of Multivariate Analysis 85: 40–53.Google Scholar
Frahm, G., Junker, M., & Szimayer, A. (2003). Elliptical copulas: Applicability and limitations. Statistics and Probability Letters 63: 275–286.Google Scholar
Giovagnoli, A. & Wynn, H.P. (1995). Multivariate dispersion orderings. Statistics and Probability Letters 22: 325–332.Google Scholar
Hickey, R.J. (1986). Concepts of dispersion in distributions: A comparative note. Journal of Applied Probability 23: 924–929.Google Scholar
Johnson, W. & Geisser, S. (1983). A predictive view of the detection and characterization of influential observations in regression analysis. Journal of the American Statistical Association 78(381): 137–144.Google Scholar
Lawrence, M.J. (1975). Inequalities of s-ordered distributions. The Annals of Statistics 3: 413–428.Google Scholar
Lewis, T. & Thompson, J.W. (1981). Dispersive distributions and the connection between dispersivity and strong unimodality. Journal of Applied Probability 18: 76–90.Google Scholar
Nelsen, R.B. (1999). An introduction to copulas. New York: Springer-Verlag.CrossRef
Rojo, J. & He, G.Z. (1991). New properties and characterizations of the dispersive ordering. Statistics and Probability Letters 11: 365–372.Google Scholar
Shaked, M. (1982). Dispersive ordering of distributions. Journal of Applied Probability 19: 310–320.Google Scholar
Shaked, M. & Shanthikumar, J.G. (1994). Stochastic orders and their applications. New York: Academic Press.