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Nonparametric variable screening for multivariate additive models

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  • Ding, Hui
  • Zhang, Jian
  • Zhang, Riquan

Abstract

In this paper we develop a novel procedure of variable screening for a multivariate additive random-effects model, based on B-spline function approximations. With these approximations, the so-called signal-to-noise ratio (SNR) can be defined to inform the importance of each covariate in the model. Then, SNR-based forward filtering is conducted on covariates by using iterative projections of the multiple response data into the space of covariates. The proposed procedure is easy to use and allows the user to pool non-linear information across heterogeneous subjects through random-effects variables. We establish an asymptotic theory on the selection consistency under some regularity conditions. By simulations, we show that the procedure has a superior performance over some existing methods in terms of sensitivity and specificity. We also apply the procedure to anti-cancer drug data, revealing a set of biomarkers that potentially influence concentrations of anti-cancer drugs in cancer cell lines.

Suggested Citation

  • Ding, Hui & Zhang, Jian & Zhang, Riquan, 2022. "Nonparametric variable screening for multivariate additive models," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:jmvana:v:192:y:2022:i:c:s0047259x22000756
    DOI: 10.1016/j.jmva.2022.105069
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    References listed on IDEAS

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    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. 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.
    3. Jian Zhang & Chao Liu & Gary Green, 2014. "Source localization with MEG data: A beamforming approach based on covariance thresholding," Biometrics, The International Biometric Society, vol. 70(1), pages 121-131, March.
    4. Fan, Jianqing & Feng, Yang & Song, Rui, 2011. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 544-557.
    5. Mathew J. Garnett & Elena J. Edelman & Sonja J. Heidorn & Chris D. Greenman & Anahita Dastur & King Wai Lau & Patricia Greninger & I. Richard Thompson & Xi Luo & Jorge Soares & Qingsong Liu & Francesc, 2012. "Systematic identification of genomic markers of drug sensitivity in cancer cells," Nature, Nature, vol. 483(7391), pages 570-575, March.
    6. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    7. Pradeep Ravikumar & John Lafferty & Han Liu & Larry Wasserman, 2009. "Sparse additive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 1009-1030, November.
    8. X. Lin & D. Zhang, 1999. "Inference in generalized additive mixed modelsby using smoothing splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 381-400, April.
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