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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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. 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.
    2. 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.
    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.

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