skip to content

Faculty of Economics

Journal Cover

Onatski, A., Moreira, M. J. and Hallin, M.

Asymptotic power of sphericity tests for high-dimensional data

Annals of Statistics

Vol. 41(3) pp. 1204-1231 (2013)

Abstract: This 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 contiguous alternatives, 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, Ben Arous and Péché [Ann. Probab. 33 (2005) 1643–1697] the limiting process is degenerate, and discrimination between the null and the alternative is asymptotically certain. When the norm is below the threshold, the limiting process is nondegenerate, and 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 va

Author links: Alexey Onatskiy  

Publisher's Link: http://dx.doi.org/10.1214/13-AOS1100SUPP



Papers and Publications



Recent Publications


Huffman, D., Raymond, C. and Shvets, J. Persistent Overconfidence and Biased Memory: Evidence from Managers American Economic Review [2022]

Elliott, M., Golub, B. and Leduc, M. V. Supply Network Formation and Fragility American Economic Review [2022]

Gallo, E. and Yan, C. Efficiency and Equilibrium in Network Games: An Experiment Review of Economics and Statistics [2023]

Ajzenman, N., Cavalcanti, T. and Da Mata, D More than Words: Leaders' Speech and Risky Behavior During a Pandemic American Economic Journal: Economic Policy [2023]