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A link-free method for testing the significance of predictors

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  • Zeng, Peng
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    Abstract

    One important step in regression analysis is to identify significant predictors from a pool of candidates so that a parsimonious model can be obtained using these significant predictors only. However, most of the existing methods assume linear relationships between response and predictors, which may be inappropriate in some applications. In this article, we discuss a link-free method that avoids specifying how the response depends on the predictors. Therefore, this method has no problem of model misspecification, and it is suitable for selecting significant predictors at the preliminary stage of data analysis. A test statistic is suggested and its asymptotic distribution is derived. Examples are used to demonstrate the proposed method.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 102 (2011)
    Issue (Month): 3 (March)
    Pages: 550-562

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    Handle: RePEc:eee:jmvana:v:102:y:2011:i:3:p:550-562

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    Related research

    Keywords: Fourier transform Nonparametric hypothesis testing Variable selection Weighted chi-squared distribution;

    References

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    1. Casella, George & Moreno, Elias, 2006. "Objective Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 157-167, March.
    2. Efang Kong & Yingcun Xia, 2007. "Variable selection for the single‐index model," Biometrika, Biometrika Trust, vol. 94(1), pages 217-229.
    3. Zhu, Yu & Zeng, Peng, 2006. "Fourier Methods for Estimating the Central Subspace and the Central Mean Subspace in Regression," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1638-1651, December.
    4. Csörgo, Sándor, 1985. "Testing for independence by the empirical characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 290-299, June.
    5. Lexin Li & R. Dennis Cook & Christopher J. Nachtsheim, 2005. "Model-free variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 285-299.
    6. Franklin Satterthwaite, 1941. "Synthesis of variance," Psychometrika, Springer, vol. 6(5), pages 309-316, October.
    7. Lexin Li, 2007. "Sparse sufficient dimension reduction," Biometrika, Biometrika Trust, vol. 94(3), pages 603-613.
    8. Zeng, Peng & Zhu, Yu, 2010. "An integral transform method for estimating the central mean and central subspaces," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 271-290, January.
    9. Hao Helen Zhang & Grace Wahba & Yi Lin & Meta Voelker & Michael Ferris & Ronald Klein & Barbara Klein, 2004. "Variable Selection and Model Building via Likelihood Basis Pursuit," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 659-672, January.
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