IDEAS home Printed from https://ideas.repec.org/p/ehu/biltok/5963.html
   My bibliography  Save this paper

Two-Stage Nonparametric Regression for Longitudinal Data

Author

Listed:
  • Ferreira García, María Eva
  • Núñez Antón, Vicente Alfredo
  • Rodríguez Poo, Juan M.

Abstract

In the analysis of longitudinal data it is of main interest to investigate the existence of group and individual effects under correlated observations across time. In this paper, we develop a nonparametric two-step procedure that enables us to estimate group effects under a very general form of correlation across time. Moreover, we propose several methods to estimate the bandwidth and show their asymptotyc optimality. Since the asymptotic distribution is untractable, we develop a randomization test that is suitable for testing the group effects. Finally, we apply the estimation procedure, the bandwidth selection criteria and the randomization test to the data from the Iowa Cochlear Implant Project.

Suggested Citation

  • Ferreira García, María Eva & Núñez Antón, Vicente Alfredo & Rodríguez Poo, Juan M., 1999. "Two-Stage Nonparametric Regression for Longitudinal Data," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    • Handle: RePEc:ehu:biltok:5963
    as

    Download full text from publisher

    File URL: https://addi.ehu.es/handle/10810/5963
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hart, Jeffrey D. & Wehrly, Thomas E., 1993. "Consistency of cross-validation when the data are curves," Stochastic Processes and their Applications, Elsevier, vol. 45(2), pages 351-361, April.
    2. Fraiman, R. & Meloche, J., 1994. "Smoothing dependent observations," Statistics & Probability Letters, Elsevier, vol. 21(3), pages 203-214, October.
    3. Vicente Núñez-Antón & Juan Rodríguez-Póo & Philippe Vieu, 1999. "Longitudinal data with nonstationary errors: a nonparametric three-stage approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 201-231, June.
    4. Ferreira, Eva & Núñez-Antón, Vicente & Rodríguez-Póo, Juan, 1997. "Kernel regression estimates of growth curves using nonstationary correlated errors," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 413-423, June.
    5. Wolfgang Härdle & Philippe Vieu, 1992. "Kernel Regression Smoothing Of Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(3), pages 209-232, May.
    6. Marron, James Stephen & Härdle, Wolfgang, 1986. "Random approximations to some measures of accuracy in nonparametric curve estimation," Journal of Multivariate Analysis, Elsevier, vol. 20(1), pages 91-113, October.
    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. Ferreira, Eva & Núñez-Antón, Vicente & Rodríguez-Póo, Juan, 1997. "Kernel regression estimates of growth curves using nonstationary correlated errors," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 413-423, June.
    2. Vicente Núñez-Antón & Juan Rodríguez-Póo & Philippe Vieu, 1999. "Longitudinal data with nonstationary errors: a nonparametric three-stage approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 201-231, June.
    3. Dale Zimmerman & Vicente Núñez-Antón & Timothy Gregoire & Oliver Schabenberger & Jeffrey Hart & Michael Kenward & Geert Molenberghs & Geert Verbeke & Mohsen Pourahmadi & Philippe Vieu & Dela Zimmerman, 2001. "Parametric modelling of growth curve data: An overview," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(1), pages 1-73, June.
    4. Karim Benhenni & Mustapha Rachdi & Yingcai Su, 2013. "The effect of the regularity of the error process on the performance of kernel regression estimators," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(6), pages 765-781, August.
    5. Zhenyu Jiang & Nengxiang Ling & Zudi Lu & Dag Tj⊘stheim & Qiang Zhang, 2020. "On bandwidth choice for spatial data density estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 817-840, July.
    6. Ayse Yilmaz & Ufuk Yolcu, 2022. "Dendritic neuron model neural network trained by modified particle swarm optimization for time‐series forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(4), pages 793-809, July.
    7. Cai, Zongwu, 2003. "Nonparametric estimation equations for time series data," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 379-390, May.
    8. Bontempi, Gianluca & Ben Taieb, Souhaib, 2011. "Conditionally dependent strategies for multiple-step-ahead prediction in local learning," International Journal of Forecasting, Elsevier, vol. 27(3), pages 689-699, July.
    9. Delsol, Laurent & Ferraty, Frédéric & Vieu, Philippe, 2011. "Structural test in regression on functional variables," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 422-447, March.
    10. Timmermans, Catherine & Delsol, Laurent & von Sachs, Rainer, 2013. "Using Bagidis in nonparametric functional data analysis: Predicting from curves with sharp local features," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 421-444.
    11. Mario Francisco-Fernandez & Juan Vilar-Fernandez, 2004. "Weighted Local Nonparametric Regression with Dependent Errors: Study of Real Private Residential Fixed Investment in the USA," Statistical Inference for Stochastic Processes, Springer, vol. 7(1), pages 69-93, March.
    12. Max Köhler & Anja Schindler & Stefan Sperlich, 2014. "A Review and Comparison of Bandwidth Selection Methods for Kernel Regression," International Statistical Review, International Statistical Institute, vol. 82(2), pages 243-274, August.
    13. BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen V.K., 2007. "Nonparametric density estimation for multivariate bounded data," LIDAM Discussion Papers CORE 2007065, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Xia, Yingcun & Li, W. K., 2002. "Asymptotic Behavior of Bandwidth Selected by the Cross-Validation Method for Local Polynomial Fitting," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 265-287, November.
    15. Federico M Bandi & Valentina Corradi & Daniel Wilhelm, 2016. "Possibly Nonstationary Cross-Validation," CeMMAP working papers 11/16, Institute for Fiscal Studies.
    16. Estévez-Pérez, Graciela, 2002. "On convergence rates for quadratic errors in kernel hazard estimation," Statistics & Probability Letters, Elsevier, vol. 57(3), pages 231-241, April.
    17. Shang, Han Lin, 2016. "A Bayesian approach for determining the optimal semi-metric and bandwidth in scalar-on-function quantile regression with unknown error density and dependent functional data," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 95-104.
    18. J. Vilar, 1995. "Kernel estimation of the regression function with random sampling times," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(1), pages 137-178, June.
    19. Xialu Liu & Zongwu Cai & Rong Chen, 2015. "Functional coefficient seasonal time series models with an application of Hawaii tourism data," Computational Statistics, Springer, vol. 30(3), pages 719-744, September.

    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:ehu:biltok:5963. 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: Alcira Macías (email available below). General contact details of provider: https://edirc.repec.org/data/deehues.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.