IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb649/sfb649dp2011-002.html
   My bibliography  Save this paper

A confidence corridor for sparse longitudinal data curves

Author

Listed:
  • Zheng, Shuzhuan
  • Yang, Lijian
  • Härdle, Wolfgang Karl

Abstract

Longitudinal data analysis is a central piece of statistics. The data are curves and they are observed at random locations. This makes the construction of a simultaneous confidence corridor (SCC) (confidence band) for the mean function a challenging task on both the theoretical and the practical side. Here we propose a method based on local linear smoothing that is implemented in the sparse (i.e., low number of nonzero coefficients) modelling situation. An SCC is constructed based on recent results obtained in applied probability theory. The precision and performance is demonstrated in a spectrum of simulations and applied to growth curve data. Technically speaking, our paper intensively uses recent insights into extreme value theory that are also employed to construct a shoal of confidence intervals (SCI).

Suggested Citation

  • Zheng, Shuzhuan & Yang, Lijian & Härdle, Wolfgang Karl, 2010. "A confidence corridor for sparse longitudinal data curves," SFB 649 Discussion Papers 2011-002, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2011-002
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/56725/1/642764220.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Wei Biao Wu & Zhibiao Zhao, 2007. "Inference of trends in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 391-410, June.
    2. Christine Cierco-Ayrolles & Alain Croquette & Céline Delmas, 2003. "Computing the Distribution of the Maximum of Gaussian Random Processes," Methodology and Computing in Applied Probability, Springer, vol. 5(4), pages 427-438, December.
    3. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    4. Jeffrey S. Morris & Raymond J. Carroll, 2006. "Wavelet‐based functional mixed models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 179-199, April.
    5. Yao, Fang, 2007. "Asymptotic distributions of nonparametric regression estimators for longitudinal or functional data," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 40-56, January.
    Full references (including those not matched with items on IDEAS)

    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. Ana-Maria Staicu & Yingxing Li & Ciprian M. Crainiceanu & David Ruppert, 2014. "Likelihood Ratio Tests for Dependent Data with Applications to Longitudinal and Functional Data Analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 932-949, December.
    2. Beran, Jan & Liu, Haiyan, 2016. "Estimation of eigenvalues, eigenvectors and scores in FDA models with dependent errors," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 218-233.
    3. Reiss Philip T. & Huang Lei & Mennes Maarten, 2010. "Fast Function-on-Scalar Regression with Penalized Basis Expansions," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-30, August.
    4. Chen, Ziqi & Hu, Jianhua & Zhu, Hongtu, 2020. "Surface functional models," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    5. Jeff Goldsmith & Vadim Zipunnikov & Jennifer Schrack, 2015. "Generalized multilevel function-on-scalar regression and principal component analysis," Biometrics, The International Biometric Society, vol. 71(2), pages 344-353, June.
    6. Qian Huang & Jinhong You & Liwen Zhang, 2022. "Efficient inference of longitudinal/functional data models with time‐varying additive structure," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 744-771, June.
    7. repec:hum:wpaper:sfb649dp2011-002 is not listed on IDEAS
    8. Yuan Wang & Jianhua Hu & Kim-Anh Do & Brian P. Hobbs, 2019. "An Efficient Nonparametric Estimate for Spatially Correlated Functional Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(1), pages 162-183, April.
    9. Li, Meng & Wang, Kehui & Maity, Arnab & Staicu, Ana-Maria, 2022. "Inference in functional linear quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    10. Yuliana Linke & Igor Borisov & Pavel Ruzankin & Vladimir Kutsenko & Elena Yarovaya & Svetlana Shalnova, 2022. "Universal Local Linear Kernel Estimators in Nonparametric Regression," Mathematics, MDPI, vol. 10(15), pages 1-28, July.
    11. Mengfei Ran & Yihe Yang, 2022. "Optimal Estimation of Large Functional and Longitudinal Data by Using Functional Linear Mixed Model," Mathematics, MDPI, vol. 10(22), pages 1-28, November.
    12. Kehui Chen & Pedro Delicado & Hans-Georg Müller, 2017. "Modelling function-valued stochastic processes, with applications to fertility dynamics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 177-196, January.
    13. Zhu, Hongxiao & Morris, Jeffrey S. & Wei, Fengrong & Cox, Dennis D., 2017. "Multivariate functional response regression, with application to fluorescence spectroscopy in a cervical pre-cancer study," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 88-101.
    14. Li Cai & Lisha Li & Simin Huang & Liang Ma & Lijian Yang, 2020. "Oracally efficient estimation for dense functional data with holiday effects," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 282-306, March.
    15. Jiang, Jiakun & Lin, Huazhen & Zhong, Qingzhi & Li, Yi, 2022. "Analysis of multivariate non-gaussian functional data: A semiparametric latent process approach," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    16. Yuliana Linke & Igor Borisov & Pavel Ruzankin & Vladimir Kutsenko & Elena Yarovaya & Svetlana Shalnova, 2024. "Multivariate Universal Local Linear Kernel Estimators in Nonparametric Regression: Uniform Consistency," Mathematics, MDPI, vol. 12(12), pages 1-23, June.
    17. Zhang, Xiaoke & Zhong, Qixian & Wang, Jane-Ling, 2020. "A new approach to varying-coefficient additive models with longitudinal covariates," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    18. Hao, Siteng & Lin, Shu-Chin & Wang, Jane-Ling & Zhong, Qixian, 2024. "Dynamic modeling for multivariate functional and longitudinal data," Journal of Econometrics, Elsevier, vol. 239(2).
    19. Haochang Shou & Vadim Zipunnikov & Ciprian M. Crainiceanu & Sonja Greven, 2015. "Structured functional principal component analysis," Biometrics, The International Biometric Society, vol. 71(1), pages 247-257, March.
    20. Li, Yehua & Qiu, Yumou & Xu, Yuhang, 2022. "From multivariate to functional data analysis: Fundamentals, recent developments, and emerging areas," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    21. Jialiang Li & Yaguang Li & Tailen Hsing, 2022. "On functional processes with multiple discontinuities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 933-972, July.

    More about this item

    Keywords

    longitudinal data; confidence band; Karhunen-Loève L2 representation; local linear estimator; extreme value; double sum; strong approximation;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

    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:zbw:sfb649:sfb649dp2011-002. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/sohubde.html .

    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.