Asymptotic Power of Sphericity Tests for High-Dimensional Data
AbstractThis paper studies the asymptotic power of tests of sphericity against perturbations in a single unknown direction as both the dimensionality of the data and the number of observations go to infinity. We establish the convergence, under the null hypothesis and the alternative, of the log ratio of the joint densities of the sample covariance eigenvalues to a Gaussian process indexed by the norm of the perturbation. When the perturbation norm is larger than the phase transition threshold studied in Baik et al. (2005), the limiting process is degenerate and discrimination between the null and the alternative is asymptotically certain. When the norm is below the threshold, the process is non-degenerate, so that the joint eigenvalue densities under the null and alternative hypotheses are mutually contiguous. Using the asymptotic theory of statistical experiments, we obtain asymptotic power envelopes and derive the asymptotic power for various sphericity tests in the contiguity region. In particular, we show that the asymptotic power of the Tracy-Widom-type tests is trivial, whereas that of the eigenvalue-based likelihood ratio test is strictly larger than the size, and close to the power envelope.
Download InfoIf 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.
Bibliographic InfoPaper provided by ULB -- Universite Libre de Bruxelles in its series Working Papers ECARES with number ECARES 2011-018.
Length: 61 p.
Date of creation: Aug 2011
Date of revision:
Publication status: Published by:
sphericity tests; large dimentionality; asymptotic power; spiker covariance; contiguity; power enveloppe; steepest descent; contour intgral representation;
This paper has been announced in the following NEP Reports:
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Onatski, Alexei, 2012. "Asymptotics of the principal components estimator of large factor models with weakly influential factors," Journal of Econometrics, Elsevier, vol. 168(2), pages 244-258.
- Gobillon, Laurent & Magnac, Thierry, 2013.
"Regional Policy Evaluation:Interactive Fixed Effects and Synthetic Controls,"
IDEI Working Papers
786, Institut d'Économie Industrielle (IDEI), Toulouse.
- Laurent Gobillon & Thierry Magnac, 2013. "Regional Policy Evaluation: Interactive Fixed Effects and Synthetic Controls," PSE Working Papers halshs-00849071, HAL.
- Gobillon, Laurent & Magnac, Thierry, 2013. "Regional Policy Evaluation:Interactive Fixed Effects and Synthetic Controls," TSE Working Papers 13-419, Toulouse School of Economics (TSE).
- Gobillon, Laurent & Magnac, Thierry, 2013. "Regional Policy Evaluation: Interactive Fixed Effects and Synthetic Controls," IZA Discussion Papers 7493, Institute for the Study of Labor (IZA).
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Benoit Pauwels).
If references are entirely missing, you can add them using this form.