Advanced Search
MyIDEAS: Login

On multivariate runs tests for randomness

Contents:

Author Info

  • Davy Paindaveine

Abstract

This paper proposes several extensions of the concept of runs to the multivariate setup, and studies the resulting tests of multivariate randomness against serial dependence. Two types of multivariate runs are defined: (i) an elliptical extension of the spherical runs proposed by Marden (1999), and (ii) an original concept of matrix-valued runs. The resulting runs tests themselves exist in various versions, one of which is a function of the number of data-based hyperplanes separating pairs of observations only. All proposed multivariate runs tests are affine-invariant and highly robust: in particular, they allow for heteroskedasticity and do not require any moment assumption. Their limiting distributions are derived under the null hypothesis and under sequences of local vector ARMA alternatives. Asymptotic relative efficiencies with respect to Gaussian Portmanteau tests are computed, and show that, while Mardentype runs tests suffer severe consistency problems, tests based on matrix-valued runs perform uniformly well for moderate-to-large dimensions. A Monte-Carlo study confirms the theoretical results and investigates the robustness properties of the proposed procedures. A real data example is also treated, and shows that combining both types of runs tests may provide some insight on the reason why rejection occurs, hence that Marden-type runs tests, despite their lack of consistency, also are of interest for practical purposes.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: https://dipot.ulb.ac.be/dspace/bitstream/2013/57547/1/RePEc_eca_wpaper_2009_002.pdf
Download Restriction: no

Bibliographic Info

Paper provided by ULB -- Universite Libre de Bruxelles in its series Working Papers ECARES with number 2009_002.

as in new window
Length:
Date of creation: 2009
Date of revision:
Publication status: Published by: ECARES
Handle: RePEc:eca:wpaper:2009_002

Contact details of provider:
Postal: Av. F.D., Roosevelt, 39, 1050 Bruxelles
Phone: (32 2) 650 30 75
Fax: (32 2) 650 44 75
Web page: http://difusion.ulb.ac.be
More information through EDIRC

Related research

Keywords: elliptical distributions; interdirections;

Other versions of this item:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Taskinen, Sara & Kankainen, Annaliisa & Oja, Hannu, 2003. "Sign test of independence between two random vectors," Statistics & Probability Letters, Elsevier, vol. 62(1), pages 9-21, March.
  2. Marc Hallin & Jean-François Ingenbleek & Madan L. Puri, 1984. "Linear serial rank tests for randomness against ARMA alternatives," ULB Institutional Repository 2013/2167, ULB -- Universite Libre de Bruxelles.
  3. Lutz Dümbgen & David E. Tyler, 2005. "On the Breakdown Properties of Some Multivariate M-Functionals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 32(2), pages 247-264.
  4. Haataja, Riina & Larocque, Denis & Nevalainen, Jaakko & Oja, Hannu, 2009. "A weighted multivariate signed-rank test for cluster-correlated data," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1107-1119, July.
  5. Thomas P. Hettmansperger, 2002. "A practical affine equivariant multivariate median," Biometrika, Biometrika Trust, vol. 89(4), pages 851-860, December.
  6. Peter Hall & J. S. Marron & Amnon Neeman, 2005. "Geometric representation of high dimension, low sample size data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 427-444.
  7. Denis Larocque & Jaakko Nevalainen & Hannu Oja, 2007. "A weighted multivariate sign test for cluster-correlated data," Biometrika, Biometrika Trust, vol. 94(2), pages 267-283.
  8. Möttönen, J. & Hüsler, J. & Oja, H., 2003. "Multivariate nonparametric tests in a randomized complete block design," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 106-129, April.
  9. Marc Hallin & Jean-Marie Dufour & Ivan Mizera, 1998. "Generalized run tests for heteroscedastic time series," ULB Institutional Repository 2013/2077, ULB -- Universite Libre de Bruxelles.
  10. Hallin, Marc & Paindaveine, Davy, 2005. "Affine-invariant aligned rank tests for the multivariate general linear model with VARMA errors," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 122-163, March.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Rainer Dyckerhoff & Christophe Ley & Davy Paindaveine, 2014. "Depth-Based Runs Tests for bivariate Central Symmetry," Working Papers ECARES 2013/76999, ULB -- Universite Libre de Bruxelles.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:eca:wpaper:2009_002. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Benoit Pauwels).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.