Affine-invariant aligned rank tests for the multivariate general linear model with VARMA errors
We develop optimal rank-based procedures for testing affine-invariant linear hypotheses on the parameters of a multivariate general linear model with elliptical VARMA errors. We propose a class of optimal procedures that are based either on residual (pseudo-)Mahalanobis signs and ranks, or on absolute interdirections and lift-interdirection ranks, i.e., on hyperplane-based signs and ranks. The Mahalanobis versions of these procedures are strictly affine-invariant, while the hyperplane-based ones are asymptotically affine-invariant. Both versions generalize the univariate signed rank procedures proposed by Hallin and Puri (J. Multivar. Anal. 50 (1994) 175), and are locally asymptotically most stringent under correctly specified radial densities. Their AREs with respect to Gaussian procedures are shown to be convex linear combinations of the AREs obtained in Hallin and Paindaveine (Ann. Statist. 30 (2002) 1103; Bernoulli 8 (2002) 787) for the pure location and purely serial models, respectively. The resulting test statistics are provided under closed form for several important particular cases, including multivariate Durbin-Watson tests, VARMA order identification tests, etc. The key technical result is a multivariate asymptotic linearity result proved in Hallin and Paindaveine (Asymptotic linearity of serial and nonserial multivariate signed rank statistics, submitted).
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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 93 (2005)
Issue (Month): 1 (March)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
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.:
- Marc Hallin & Madan Lal Puri, 1995. "A multivariate Wald-Wolfowitz rank test against serial dependence," ULB Institutional Repository 2013/2051, ULB -- Universite Libre de Bruxelles.
- Marc Hallin & Bernard Garel, 1999. "Rank-based AR order identification," ULB Institutional Repository 2013/2087, ULB -- Universite Libre de Bruxelles.
- Hannu Oja, 1999. "Affine Invariant Multivariate Sign and Rank Tests and Corresponding Estimates: a Review," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(3), pages 319-343.
- Marc Hallin & Jean-François Ingenbleek & Madan Lal Puri, 1989.
"Asymptotically most powerful rank tests for multivariate randomness against serial dependence,"
ULB Institutional Repository
2013/2019, ULB -- Universite Libre de Bruxelles.
- Hallin, Marc & Ingenbleek, Jean-Francois & Puri, Madan L., 1989. "Asymptotically most powerful rank tests for multivariate randomness against serial dependence," Journal of Multivariate Analysis, Elsevier, vol. 30(1), pages 34-71, July.
- Hallin, M. & Puri, M. L., 1994.
"Aligned Rank Tests for Linear Models with Autocorrelated Error Terms,"
Journal of Multivariate Analysis,
Elsevier, vol. 50(2), pages 175-237, August.
- Hallin, M. & Puri, L.M., 1992. "Aligned Rank tests for Linear Models with Autocorrelated Error Terms," Papers 9202, Universite Libre de Bruxelles - C.E.M.E..
- Marc Hallin & Madan Lal Puri, 1994. "Aligned rank tests for linear models with autocorrelated errors," ULB Institutional Repository 2013/2045, ULB -- Universite Libre de Bruxelles.
- Garel, B. & Hallin, M., 1992.
"Local Asymptotic Normality of Multivariate ARMA Processes with a Linear Trend,"
9213, Universite Libre de Bruxelles - C.E.M.E..
- Bernard Garel & Marc Hallin, 1995. "Local asymptotic normality of multivariate ARMA processes with a linear trend," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 551-579, September.
- Marc Hallin & Bernard Garel, 1995. "Local asymptotic normality of multivariate ARMA processes with a linear trend," ULB Institutional Repository 2013/2053, ULB -- Universite Libre de Bruxelles.
- Marc Hallin & Bas Werker, 2003.
"Semiparametric efficiency, distribution-freeness, and invariance,"
ULB Institutional Repository
2013/2119, ULB -- Universite Libre de Bruxelles.
- Hallin, M. & Werker, B.J.M., 2003. "Semiparametric efficiency, distribution-freeness and invariance," Other publications TiSEM fe20db00-786a-4261-9999-6, Tilburg University, School of Economics and Management.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:93:y:2005:i:1:p:122-163. 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: (Shamier, Wendy)
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.