IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v101y2014i3p567-585..html
   My bibliography  Save this article

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

Author

Listed:
  • 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.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/asu025
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. Ming-Chin Hung & William H. Swallow, 2000. "Use of Binomial Group Testing in Tests of Hypotheses for Classification or Quantitative Covariables," Biometrics, The International Biometric Society, vol. 56(1), pages 204-212, March.
    3. 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.
    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. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Nguyen, Ngoc T. & Bish, Ebru K. & Bish, Douglas R., 2021. "Optimal pooled testing design for prevalence estimation under resource constraints," Omega, Elsevier, vol. 105(C).
    5. 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.
    6. 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.
    7. Kim, Kun Ho & Chao, Shih-Kang & Härdle, Wolfgang Karl, 2020. "Simultaneous Inference of the Partially Linear Model with a Multivariate Unknown Function," IRTG 1792 Discussion Papers 2020-008, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    8. Dette, Holger & Marchlewski, Mareen, 2007. "A test for the parametric form of the variance function in apartial linear regression model," Technical Reports 2007,26, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    9. 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.
    10. Ferraccioli, Federico & Sangalli, Laura M. & Finos, Livio, 2022. "Some first inferential tools for spatial regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    11. Cui, Xia & Lu, Ying & Peng, Heng, 2017. "Estimation of partially linear regression models under the partial consistency property," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 103-121.
    12. Yuejin Zhou & Yebin Cheng & Wenlin Dai & Tiejun Tong, 2018. "Optimal difference-based estimation for partially linear models," Computational Statistics, Springer, vol. 33(2), pages 863-885, June.
    13. Zhu, Xuehu & Wang, Tao & Zhao, Junlong & Zhu, Lixing, 2017. "Inference for biased transformation models," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 105-120.
    14. Kim, Namhyun & W. Saart, Patrick, 2021. "Estimation in partially linear semiparametric models with parametric and/or nonparametric endogeneity," Cardiff Economics Working Papers E2021/9, Cardiff University, Cardiff Business School, Economics Section.
    15. Lu Lin & Lili Liu & Xia Cui & Kangning Wang, 2021. "A generalized semiparametric regression and its efficient estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 1-24, March.
    16. Aifen Feng & Xiaogai Chang & Jingya Fan & Zhengfen Jin, 2023. "Application of LADMM and As-LADMM for a High-Dimensional Partially Linear Model," Mathematics, MDPI, vol. 11(19), pages 1-14, October.
    17. B. Ettinger & S. Perotto & L. M. Sangalli, 2016. "Spatial regression models over two-dimensional manifolds," Biometrika, Biometrika Trust, vol. 103(1), pages 71-88.
    18. Lian, Heng & Liang, Hua, 2016. "Separation of linear and index covariates in partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 56-70.
    19. Hu Yang & Ning Li & Jing Yang, 2020. "A robust and efficient estimation and variable selection method for partially linear models with large-dimensional covariates," Statistical Papers, Springer, vol. 61(5), pages 1911-1937, October.
    20. Huang, Zhensheng & Pang, Zhen & Hu, Tao, 2013. "Testing structural change in partially linear single-index models with error-prone linear covariates," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 121-133.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:oup:biomet:v:101:y:2014:i:3:p:567-585.. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.