Strong Consistency of Log-Likelihood-Based Information Criterion in High-Dimensional Canonical Correlation Analysis

Ryoya Oda (), Hirokazu Yanagihara and Yasunori Fujikoshi
Additional contact information
Ryoya Oda: Hiroshima University
Hirokazu Yanagihara: Hiroshima University
Yasunori Fujikoshi: Hiroshima University

Sankhya A: The Indian Journal of Statistics, 2021, vol. 83, issue 1, No 4, 109-127

Abstract: Abstract We consider the strong consistency of a log-likelihood-based information criterion in a normality-assumed canonical correlation analysis between q- and p-dimensional random vectors for a high-dimensional case such that the sample size n and number of dimensions p are large but p/n is less than 1. In general, strong consistency is a stricter property than weak consistency; thus, sufficient conditions for the former do not always coincide with those for the latter. We derive the sufficient conditions for the strong consistency of this log-likelihood-based information criterion for the high-dimensional case. It is shown that the sufficient conditions for strong consistency of several criteria are the same as those for weak consistency obtained by Yanagihara et al. (J. Multivariate Anal. 157, 70–86: 2017).

Keywords: Canonical correlation analysis; High-dimensional asymptotic framework; Strong consistency; Variable selection; 62H20; 62E20 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s13171-019-00174-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sankha:v:83:y:2021:i:1:d:10.1007_s13171-019-00174-3

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/13171

DOI: 10.1007/s13171-019-00174-3

Access Statistics for this article

Sankhya A: The Indian Journal of Statistics is currently edited by Dipak Dey

More articles in Sankhya A: The Indian Journal of Statistics from Springer, Indian Statistical Institute
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().