Hiroshima Mathematical Journal

Consistency of log-likelihood-based information criteria for selecting variables in high-dimensional canonical correlation analysis under nonnormality

Keisuke Fukui

Full-text: Open access

Abstract

The purpose of this paper is to clarify the conditions for consistency of the log-likelihood-based information criteria in canonical correlation analysis of q- and p-dimensional random vectors when the dimension p is large but does not exceed the sample size. Although the vector of observations is assumed to be normally distributed, we do not know whether the underlying distribution is actually normal. Therefore, conditions for consistency are evaluated in a high-dimensional asymptotic framework when the underlying distribution is not normal.

Article information

Source
Hiroshima Math. J., Volume 45, Number 2 (2015), 175-205.

Dates
First available in Project Euclid: 10 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1439219708

Digital Object Identifier
doi:10.32917/hmj/1439219708

Mathematical Reviews number (MathSciNet)
MR3379002

Zentralblatt MATH identifier
1327.62339

Subjects
Primary: 62H12: Estimation
Secondary: 62H20: Measures of association (correlation, canonical correlation, etc.)

Keywords
AIC assumption of normality bias-corrected AIC BIC consistent AIC high-dimensional asymptotic framework HQC nonnormality selection of redundancy model selection probability

Citation

Fukui, Keisuke. Consistency of log-likelihood-based information criteria for selecting variables in high-dimensional canonical correlation analysis under nonnormality. Hiroshima Math. J. 45 (2015), no. 2, 175--205. doi:10.32917/hmj/1439219708. https://projecteuclid.org/euclid.hmj/1439219708


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