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Smoothing and mixed models

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  • M. P. Wand

    (Harvard University)

Abstract

Summary Smoothing methods that use. basis functions with penalisation can be formulated as maximum likelihood estimators and best predictors in a mixed model framework. Such connections are at least a quarter of a century old but, perhaps with the advent of mixed model software, have led to a paradigm shift in the field of smoothing. The reason is that most, perhaps all, models involving smoothing can be expressed as a mixed model and hence enjoy the benefit of the growing body of methodology and software for general mixed model analysis. The handling of other complications such as clustering, missing data and measurement error is generally quite straightforward with mixed model representations of smoothing.

Suggested Citation

  • M. P. Wand, 2003. "Smoothing and mixed models," Computational Statistics, Springer, vol. 18(2), pages 223-249, July.
    • Handle: RePEc:spr:compst:v:18:y:2003:i:2:d:10.1007_s001800300142
    DOI: 10.1007/s001800300142
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    References listed on IDEAS

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    1. Yuedong Wang, 1998. "Mixed effects smoothing spline analysis of variance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 159-174.
    2. Wing‐Kam Fung & Zhong‐Yi Zhu & Bo‐Cheng Wei & Xuming He, 2002. "Influence diagnostics and outlier tests for semiparametric mixed models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 565-579, August.
    3. Arũnas P. Verbyla & Brian R. Cullis & Michael G. Kenward & Sue J. Welham, 1999. "The Analysis of Designed Experiments and Longitudinal Data by Using Smoothing Splines," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(3), pages 269-311.
    4. X. Lin & D. Zhang, 1999. "Inference in generalized additive mixed modelsby using smoothing splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 381-400, April.
    5. Brent A. Coull & David Ruppert & M. P. Wand, 2001. "Simple Incorporation of Interactions into Additive Models," Biometrics, The International Biometric Society, vol. 57(2), pages 539-545, June.
    6. Ke C. & Wang Y., 2001. "Semiparametric Nonlinear Mixed-Effects Models and Their Applications," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1272-1298, December.
    7. Gareth M. James & Trevor J. Hastie, 2001. "Functional linear discriminant analysis for irregularly sampled curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 533-550.
    8. Antoniadis A. & Fan J., 2001. "Regularization of Wavelet Approximations," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 939-967, September.
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