IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v114y2013icp288-302.html

Kernel smoothers and bootstrapping for semiparametric mixed effects models

Author

Listed:
  • González Manteiga, Wenceslao
  • Lombardía, María José
  • Martínez Miranda, María Dolores
  • Sperlich, Stefan

Abstract

While today linear mixed effects models are frequently used tools in different fields of statistics, in particular for studying data with clusters, longitudinal or multi-level structure, the nonparametric formulation of mixed effects models is still quite recent. In this paper we discuss and compare different nonparametric estimation methods. In this context we introduce a computationally inexpensive bootstrap method, which is used to estimate local mean squared errors, to construct confidence intervals and to find locally optimal smoothing parameters. The theoretical considerations are accompanied by the provision of algorithms and simulation studies of the finite sample behavior of the methods. We show that our confidence intervals have good coverage probabilities, and that our bandwidth selection method succeeds to minimize the mean squared error for the nonparametric function locally.

Suggested Citation

  • González Manteiga, Wenceslao & Lombardía, María José & Martínez Miranda, María Dolores & Sperlich, Stefan, 2013. "Kernel smoothers and bootstrapping for semiparametric mixed effects models," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 288-302.
    • Handle: RePEc:eee:jmvana:v:114:y:2013:i:c:p:288-302
    DOI: 10.1016/j.jmva.2012.08.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X12002035
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2012.08.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Gonzalez Manteiga, W. & Martinez Miranda, M. D. & Perez Gonzalez, A., 2004. "The choice of smoothing parameter in nonparametric regression through Wild Bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 487-515, October.
    2. Wangli Xu & Lixing Zhu, 2009. "Kernel‐based Generalized Cross‐validation in Non‐parametric Mixed‐effect Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 229-247, June.
    3. Chris Elbers & Jean O. Lanjouw & Peter Lanjouw, 2003. "Micro--Level Estimation of Poverty and Inequality," Econometrica, Econometric Society, vol. 71(1), pages 355-364, January.
    4. Jiming Jiang & P. Lahiri, 2006. "Mixed model prediction and small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-96, June.
    5. Naisyin Wang, 2003. "Marginal nonparametric kernel regression accounting for within-subject correlation," Biometrika, Biometrika Trust, vol. 90(1), pages 43-52, March.
    6. Kani Chen & Zhezhen Jin, 2005. "Local polynomial regression analysis of clustered data," Biometrika, Biometrika Trust, vol. 92(1), pages 59-74, March.
    7. Gerda Claeskens & Jeffrey Hart, 2009. "Rejoinder on: Goodness-of-fit tests in mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 265-270, August.
    8. María José Lombardía & Stefan Sperlich, 2008. "Semiparametric inference in generalized mixed effects models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 913-930, November.
    9. Gerda Claeskens & Jeffrey Hart, 2009. "Goodness-of-fit tests in mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 213-239, August.
    10. Xihong Lin & Raymond J. Carroll, 2006. "Semiparametric estimation in general repeated measures problems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 69-88, February.
    11. J. D. Opsomer & G. Claeskens & M. G. Ranalli & G. Kauermann & F. J. Breidt, 2008. "Non‐parametric small area estimation using penalized spline regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 265-286, February.
    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. Stefan Sperlich & Raoul Theler, 2015. "Modeling heterogeneity: a praise for varying-coefficient models in causal analysis," Computational Statistics, Springer, vol. 30(3), pages 693-718, September.
    2. Stefan Sperlich, 2013. "Comments on: Model-free model-fitting and predictive distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 227-233, June.
    3. Nikos Tzavidis & Li‐Chun Zhang & Angela Luna & Timo Schmid & Natalia Rojas‐Perilla, 2018. "From start to finish: a framework for the production of small area official statistics," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 927-979, October.

    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. José Lombardía, María & Sperlich, Stefan, 2012. "A new class of semi-mixed effects models and its application in small area estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2903-2917.
    2. Stefan Sperlich & María José Lombardía, 2010. "Local polynomial inference for small area statistics: estimation, validation and prediction," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(5), pages 633-648.
    3. Stefan Sperlich, 2013. "Comments on: Model-free model-fitting and predictive distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 227-233, June.
    4. Salvati, Nicola & Chandra, Hukum & Giovanna Ranalli, M. & Chambers, Ray, 2010. "Small area estimation using a nonparametric model-based direct estimator," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2159-2171, September.
    5. Xuemei Hu & Weiming Yang, 2019. "Semi-parametric small area inference in generalized semi-varying coefficient mixed effects models," Statistical Papers, Springer, vol. 60(4), pages 1039-1058, August.
    6. Tang, Min & Slud, Eric V. & Pfeiffer, Ruth M., 2014. "Goodness of fit tests for linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 176-193.
    7. Gonzales Manteiga, Wenceslao & Maria Dolores, Martinez Miranda & Van Keilegom, Ingrid, 2012. "Goodness-of-fit Test in Parametric Mixed-Effects Models based on the Estimation of the Error Distribution," LIDAM Discussion Papers ISBA 2012022, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Charnigo, Richard & Feng, Limin & Srinivasan, Cidambi, 2015. "Nonparametric and semiparametric compound estimation in multiple covariates," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 179-196.
    9. Al Kadiri, M. & Carroll, R.J. & Wand, M.P., 2010. "Marginal longitudinal semiparametric regression via penalized splines," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1242-1252, August.
    10. Liugen Xue, 2010. "Empirical Likelihood Local Polynomial Regression Analysis of Clustered Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 644-663, December.
    11. Patrick Munyangabo & Anthony Waititu & Anthony Kibira Wanjoya, 2019. "Estimation of Nested Error Non-parametric Unit Level Model," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 8(1), pages 1-3.
    12. Ke Yang, 2013. "An Improved Local-linear Estimator For Nonparametric Regression With Autoregressive Errors," Economics Bulletin, AccessEcon, vol. 33(1), pages 19-27.
    13. J. N. K. Rao, 2015. "Inferential issues in model-based small area estimation: some new developments," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 16(4), pages 491-510, December.
    14. N. Salvati & N. Tzavidis & M. Pratesi & R. Chambers, 2012. "Small area estimation via M-quantile geographically weighted regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 1-28, March.
    15. Militino, A.F. & Goicoa, T. & Ugarte, M.D., 2012. "Estimating the percentage of food expenditure in small areas using bias-corrected P-spline based estimators," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2934-2948.
    16. Enrico Fabrizi & Caterina Giusti & Nicola Salvati & Nikos Tzavidis, 2014. "Mapping average equivalized income using robust small area methods," Papers in Regional Science, Wiley Blackwell, vol. 93(3), pages 685-701, August.
    17. Zhang, Junhua & Feng, Sanying & Li, Gaorong & Lian, Heng, 2011. "Empirical likelihood inference for partially linear panel data models with fixed effects," Economics Letters, Elsevier, vol. 113(2), pages 165-167.
    18. Li, Cong & Liang, Zhongwen, 2015. "Asymptotics for nonparametric and semiparametric fixed effects panel models," Journal of Econometrics, Elsevier, vol. 185(2), pages 420-434.
    19. Isabel Proença & Stefan Sperlich & Duygu Savaşcı, 2015. "Semi-mixed effects gravity models for bilateral trade," Empirical Economics, Springer, vol. 48(1), pages 361-387, February.
    20. Baldermann, Claudia & Salvati, Nicola & Schmid, Timo, 2016. "Robust small area estimation under spatial non-stationarity," Discussion Papers 2016/5, Free University Berlin, School of Business & Economics.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:eee:jmvana:v:114:y:2013:i:c:p:288-302. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.