skip to content

Faculty of Economics

Journal Cover

Johnstone, I. M. and Onatski, A.

Testing in High-dimensional Spiked Models

Annals of Statistics, forthcoming

Abstract: We consider the five classes of multivariate statistical problems identified by James (1964), which together cover much of classical multivariate analysis, plus a simpler limiting case, symmetric matrix denoising. Each of James’ problems involves the eigenvalues of H -1 E where H and E are proportional to high dimensional Wishart matrices. Under the null hypothesis, both Wisharts are central with identity covariance. Under the alternative, the non-centrality or the covariance parameter of H has a single eigenvalue, a spike, that stands alone. When the spike is smaller than a case-specific phase transition threshold, none of the sample eigenvalues separate from the bulk, making the testing problem challenging. Using a unified strategy for the six cases, we show that the log likelihood ratio processes parameterized by the value of the sub-critical spike converge to Gaussian processes with logarithmic correlation. We then derive asymptotic power envelopes for tests for the presence of a spike.

Keywords: likelihood ratio test, hypergeometric function, principal components analysis, canonical correlations, matrix denoising, multiple response regression

Author links: Alexey Onatskiy  

Publisher's Link: https://www.e-publications.org/ims/submission/AOS/user/submissionFile/30298?confirm=5e52e6aa


Cambridge Working Paper in Economics Version of Paper: Testing in High-Dimensional Spiked Models, Johnstone, I. M. and Onatski, A., (2018)

Papers and Publications



Recent Publications


Fruehwirth, J., Iyer, S. and Zhang, A. Religion and Depression in Adolescence Journal of Political Economy, forthcoming [2019]

Faraglia, E., Marcet, A., Oikonomou, R. and Scott, A. Government Debt management: the Short and the Long of it Review of Economic Studies, accepted [2018]

Elliott, M. and Golub, B. A network approach to public goods accepted, Journal of Political Economy [2018]