Likelihood ratio test for partial sphericity in high and ultra-high dimensions

Liliana Forzani, Antonella Gieco, Carlos Tolmasky

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We consider, in the setting of p and n large, sample covariance matrices whose population counterparts follow a spiked population model, i.e., with the exception of the first (largest) few, all the population eigenvalues are equal. We study the asymptotic distribution of the partial maximum likelihood ratio statistic and use it to test for the dimension of the population spike subspace. Furthermore, we extend this to the ultra-high-dimensional case, i.e., p>;n. A thorough study of the power of the test gives a correction that allows us to test for the dimension of the population spike subspace even for values of the limit of p/n close to 1, a setting where other approaches have proved to be deficient.

Original languageEnglish (US)
Pages (from-to)18-38
Number of pages21
JournalJournal of Multivariate Analysis
Volume159
DOIs
StatePublished - Jul 1 2017

Bibliographical note

Funding Information:
We would like to gratefully thank the Editor and an anonymous referee for her/his comments which have greatly improved our manuscript. This work was supported by the SECTEI grant 2010-072-14, by the UNL grants 500-040, 501-499 and 500-062; by the CONICET grant PIP 742 and by the ANPCYT grant PICT 2012-2590.

Keywords

  • High-dimensional statistics
  • Principal component analysis
  • Random matrix theory
  • Sample covariance matrix
  • Spiked population model

Fingerprint Dive into the research topics of 'Likelihood ratio test for partial sphericity in high and ultra-high dimensions'. Together they form a unique fingerprint.

Cite this