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Nonparametric Additive Regression for High-Dimensional Group Testing Data

Author

Listed:
  • Xinlei Zuo

    (School of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, China)

  • Juan Ding

    (School of Mathematics, Hohai University, Nanjing 210098, China)

  • Junjian Zhang

    (School of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, China)

  • Wenjun Xiong

    (School of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, China)

Abstract

Group testing has been verified as a cost-effective and time-efficient approach, where the individual samples are pooled with a predefined group size for subsequent testing. Recent research has explored the integration of covariate information to improve the modeling of the group testing data. While existing works for high-dimensional data primarily focus on parametric models, this study considers a more flexible generalized nonparametric additive model. Nonlinear components are approximated using B-splines and model estimation under the sparsity assumption is derived employing group lasso. Theoretical results demonstrate that our method selects the true model with a high probability and provides consistent estimates. Numerical studies are conducted to illustrate the good performance of our proposed method, using both simulated and real data.

Suggested Citation

  • Xinlei Zuo & Juan Ding & Junjian Zhang & Wenjun Xiong, 2024. "Nonparametric Additive Regression for High-Dimensional Group Testing Data," Mathematics, MDPI, vol. 12(5), pages 1-21, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:686-:d:1346583
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    References listed on IDEAS

    as
    1. S. Vansteelandt & E. Goetghebeur & T. Verstraeten, 2000. "Regression Models for Disease Prevalence with Diagnostic Tests on Pools of Serum Samples," Biometrics, The International Biometric Society, vol. 56(4), pages 1126-1133, December.
    2. A. Delaigle & P. Hall & J. R. Wishart, 2014. "New approaches to nonparametric and semiparametric regression for univariate and multivariate group testing data," Biometrika, Biometrika Trust, vol. 101(3), pages 567-585.
    3. Bilder, Christopher R. & Tebbs, Joshua M. & Chen, Peng, 2010. "Informative Retesting," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 942-955.
    4. Peng Chen & Joshua M. Tebbs & Christopher R. Bilder, 2009. "Group Testing Regression Models with Fixed and Random Effects," Biometrics, The International Biometric Society, vol. 65(4), pages 1270-1278, December.
    5. Karl B. Gregory & Dewei Wang & Christopher S. McMahan, 2019. "Adaptive elastic net for group testing," Biometrics, The International Biometric Society, vol. 75(1), pages 13-23, March.
    6. Hae-Young Kim & Michael G. Hudgens & Jonathan M. Dreyfuss & Daniel J. Westreich & Christopher D. Pilcher, 2007. "Comparison of Group Testing Algorithms for Case Identification in the Presence of Test Error," Biometrics, The International Biometric Society, vol. 63(4), pages 1152-1163, December.
    7. Christopher S. McMahan & Joshua M. Tebbs & Timothy E. Hanson & Christopher R. Bilder, 2017. "Bayesian regression for group testing data," Biometrics, The International Biometric Society, vol. 73(4), pages 1443-1452, December.
    8. Takuma Yoshida & Kanta Naito, 2014. "Asymptotics for penalised splines in generalised additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(2), pages 269-289, June.
    9. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    10. D. Wang & C. S. McMahan & C. M. Gallagher & K. B. Kulasekera, 2014. "Semiparametric group testing regression models," Biometrika, Biometrika Trust, vol. 101(3), pages 587-598.
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