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Robust multivariate association and dimension reduction using density divergences

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  • Iaci, Ross
  • Sriram, T.N.

Abstract

In this article, we introduce two new families of multivariate association measures based on power divergence and alpha divergence that recover both linear and nonlinear dependence relationships between multiple sets of random vectors. Importantly, this novel approach not only characterizes independence, but also provides a smooth bridge between well-known distances that are inherently robust against outliers. Algorithmic approaches are developed for dimension reduction and the selection of the optimal robust association index. Extensive simulation studies are performed to assess the robustness of these association measures under different types and proportions of contamination. We illustrate the usefulness of our methods in application by analyzing two socioeconomic datasets that are known to contain outliers or extreme observations. Some theoretical properties, including the consistency of the estimated coefficient vectors, are investigated and computationally efficient algorithms for our nonparametric methods are provided.

Suggested Citation

  • Iaci, Ross & Sriram, T.N., 2013. "Robust multivariate association and dimension reduction using density divergences," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 281-295.
  • Handle: RePEc:eee:jmvana:v:117:y:2013:i:c:p:281-295
    DOI: 10.1016/j.jmva.2013.03.004
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    References listed on IDEAS

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    1. Hubert, Mia & Rousseeuw, Peter & Verdonck, Tim, 2009. "Robust PCA for skewed data and its outlier map," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2264-2274, April.
    2. Witten Daniela M & Tibshirani Robert J., 2009. "Extensions of Sparse Canonical Correlation Analysis with Applications to Genomic Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-29, June.
    3. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    4. Xiangrong Yin & R. Dennis Cook, 2005. "Direction estimation in single-index regressions," Biometrika, Biometrika Trust, vol. 92(2), pages 371-384, June.
    5. Yin, Xiangrong, 2004. "Canonical correlation analysis based on information theory," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 161-176, November.
    6. Iaci, Ross & Yin, Xiangrong & Sriram, T. N & Klingenberg, Christian Peter, 2008. "An Informational Measure of Association and Dimension Reduction for Multiple Sets and Groups With Applications in Morphometric Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1166-1176.
    7. Mario Romanazzi, 1992. "Influence in canonical correlation analysis," Psychometrika, Springer;The Psychometric Society, vol. 57(2), pages 237-259, June.
    8. 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.
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    Cited by:

    1. Iaci, Ross & Yin, Xiangrong & Zhu, Lixing, 2016. "The Dual Central Subspaces in dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 178-189.
    2. 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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