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New approaches to nonparametric and semiparametric regression for univariate and multivariate group testing data

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  • A. Delaigle
  • P. Hall
  • J. R. Wishart

Abstract

We consider nonparametric and semiparametric estimation of a conditional probability curve in the case of group testing data, where the individuals are pooled randomly into groups and only the pooled data are available. We derive a nonparametric weighted estimator that has optimality properties accounting for group sizes, and show how to extend it to multivariate settings, including the partially linear model. In the group testing context, it is natural to assume that the probability curve depends on the covariates only through a linear combination of them. Motivated by this condition, we develop a nonparametric estimator based on the single-index model. We study theoretical properties of the proposed estimators and derive data-driven procedures. Practical properties of the methods are demonstrated via real and simulated examples, and our estimators are shown to have smaller median integrated square error than existing competitors.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:101:y:2014:i:3:p:567-585.
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    File URL: http://hdl.handle.net/10.1093/biomet/asu025
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    References listed on IDEAS

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    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.
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    4. Dewei Wang & Haiming Zhou & K. B. Kulasekera, 2013. "A semi-local likelihood regression estimator of the proportion based on group testing data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(1), pages 209-221, March.
    5. Delaigle, Aurore & Meister, Alexander, 2011. "Nonparametric Regression Analysis for Group Testing Data," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 640-650.
    6. Delaigle, Aurore & Fan, Jianqing & Carroll, Raymond J., 2009. "A Design-Adaptive Local Polynomial Estimator for the Errors-in-Variables Problem," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 348-359.
    7. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    8. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    9. Xianzheng Huang & Joshua M. Tebbs, 2009. "On Latent-Variable Model Misspecification in Structural Measurement Error Models for Binary Response," Biometrics, The International Biometric Society, vol. 65(3), pages 710-718, September.
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    Cited by:

    1. 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.
    2. Chase N. Joyner & Christopher S. McMahan & Joshua M. Tebbs & Christopher R. Bilder, 2020. "From mixed effects modeling to spike and slab variable selection: A Bayesian regression model for group testing data," Biometrics, The International Biometric Society, vol. 76(3), pages 913-923, September.
    3. Xianzheng Huang & Md Shamim Sarker Warasi, 2017. "Maximum Likelihood Estimators in Regression Models for Error-prone Group Testing Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 918-931, December.
    4. 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.

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