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Asymptotic properties of canonical correlation analysis for one group with additional observations

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  • Yamada, Tomoya

Abstract

We develop canonical correlation analysis in the context of two-step monotone incomplete data drawn from Np+q(μ,Σ), a multivariate normal population with mean μ and covariance matrix Σ. Our data consist of n observations on each group and an additional N−n observations on only one group, where all observations are mutually independent. We perform the canonical correlation analysis using the maximum likelihood estimators, with the monotone incomplete data, of μ and Σ. Further, we derive the asymptotic expansion of the distributions of the canonical correlations and the limiting distributions of the canonical vectors, and we compare them with the results of a typical canonical correlation.

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  • Yamada, Tomoya, 2013. "Asymptotic properties of canonical correlation analysis for one group with additional observations," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 389-401.
    • Handle: RePEc:eee:jmvana:v:114:y:2013:i:c:p:389-401
    DOI: 10.1016/j.jmva.2012.08.001
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    References listed on IDEAS

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    5. Taskinen, Sara & Croux, Christophe & Kankainen, Annaliisa & Ollila, Esa & Oja, Hannu, 2006. "Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 359-384, February.
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    Cited by:

    1. Tomoya Yamada & Megan Romer & Donald Richards, 2015. "Kurtosis tests for multivariate normality with monotone incomplete data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 532-557, September.
    2. Tsukada, Shin-ichi, 2014. "Asymptotic expansion for distribution of the trace of a covariance matrix under a two-step monotone incomplete sample," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 206-219.

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