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A semiparametric approach to canonical analysis

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  • Yingcun Xia

Abstract

Summary. Classical canonical correlation analysis is one of the fundamental tools in statistics to investigate the linear association between two sets of variables. We propose a method, called semiparametric canonical analysis, to generalize canonical correlation analysis to incorporate the important non‐linear association. Semiparametric canonical analysis is easy to implement and interpret. Statistical properties are proved. A consistent estimation method is developed. Selection of significant semiparametric canonical analysis components is discussed. Simulations suggest that the methods proposed have satisfactory performance in finite samples. One environmental data set and one data set in social science are investigated, in which non‐linear canonical associations are observed and interpreted.

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  • Yingcun Xia, 2008. "A semiparametric approach to canonical analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 519-543, July.
    • Handle: RePEc:bla:jorssb:v:70:y:2008:i:3:p:519-543
    DOI: 10.1111/j.1467-9868.2007.00647.x
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    Cited by:

    1. Denis Agniel & Tianxi Cai, 2017. "Analysis of multiple diverse phenotypes via semiparametric canonical correlation analysis," Biometrics, The International Biometric Society, vol. 73(4), pages 1254-1265, December.
    2. Ross Iaci & T.N. Sriram & Xiangrong Yin, 2010. "Multivariate Association and Dimension Reduction: A Generalization of Canonical Correlation Analysis," Biometrics, The International Biometric Society, vol. 66(4), pages 1107-1118, December.
    3. Kun Chen & Yanyuan Ma, 2017. "Analysis of Double Single Index Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 1-20, March.

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