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Inference in smoothing spline analysis of variance

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  • Wensheng Guo

Abstract

Summary. Smoothing spline analysis of variance decomposes a multivariate function into additive components. This decomposition not only provides an efficient way to model a multivariate function but also leads to meaningful inference by testing whether a certain component equals 0. No formal procedure is yet available to test such a hypothesis. We propose an asymptotic method based on the likelihood ratio to test whether a functional component is 0. This test allows us to choose an optimal model and to compare groups of curves. We first develop the general theory by exploiting the connection between mixed effects models and smoothing splines. We then apply this to compare two groups of curves and to select an optimal model in a two‐dimensional problem. A small simulation is used to assess the finite sample performance of the likelihood ratio test.

Suggested Citation

  • Wensheng Guo, 2002. "Inference in smoothing spline analysis of variance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 887-898, October.
    • Handle: RePEc:bla:jorssb:v:64:y:2002:i:4:p:887-898
    DOI: 10.1111/1467-9868.00367
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    Cited by:

    1. de Uña Álvarez, Jacobo & Roca Pardiñas, Javier, 2009. "Additive models in censored regression," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3490-3501, July.
    2. Roca-Pardinas, Javier & Cadarso-Suarez, Carmen & Tahoces, Pablo G. & Lado, Maria J., 2008. "Assessing continuous bivariate effects among different groups through nonparametric regression models: An application to breast cancer detection," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1958-1970, January.
    3. Jaroslaw Harezlak & Louise M. Ryan & Jay N. Giedd & Nicholas Lange, 2005. "Individual and Population Penalized Regression Splines for Accelerated Longitudinal Designs," Biometrics, The International Biometric Society, vol. 61(4), pages 1037-1048, December.
    4. Antoniadis, Anestis & Sapatinas, Theofanis, 2007. "Estimation and inference in functional mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4793-4813, June.
    5. Sue J. Welham & Brian R. Cullis & Michael G. Kenward & Robin Thompson, 2006. "The Analysis of Longitudinal Data Using Mixed Model L-Splines," Biometrics, The International Biometric Society, vol. 62(2), pages 392-401, June.
    6. Jiang Lin & Daowen Zhang & Marie Davidian, 2006. "Smoothing Spline-Based Score Tests for Proportional Hazards Models," Biometrics, The International Biometric Society, vol. 62(3), pages 803-812, September.

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