Functional Data Analysis in Designed Experiments

  • Bairu ZhangEmail author
  • Heiko Großmann
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)


F-type tests for functional ANOVA models implicitly assume that the response curves are generated by a completely randomized design. By using the split-plot design as an example it is illustrated how these tests can be extended to more complex ANOVA models. In order to derive the test statistics and their approximate null distributions, Hasse diagrams for representing the structure of the experiment are combined with a stochastic process perspective. The application of the more general F-type tests is illustrated for simulated data.


Covariance Function Functional Data Null Distribution Treatment Factor Hasse Diagram 
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  1. 1.
    Antoniadis, A., Sapatinas, T.: Estimation and inference in functional mixed-effects models. Comput. Stat. Data Anal. 51 (10), 4793–4813 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Bailey, R.A.: Design of Comparative Experiments. Cambridge University Press, Cambridge (2008)CrossRefzbMATHGoogle Scholar
  3. 3.
    Fan, J.Q., Zhang, J.T.: Two-step estimation of functional linear models with applications to longitudinal data. J. R. Stat. Soc. Ser. B. 62 (2), 303–322 (2000)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Faraway, J.J.: Regression analysis for a functional response. Technometrics 39 (3), 254–261 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Guo, W.: Functional mixed effects models. Biometrics 58 (1), 121–128 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Hsing, T., Eubank, R.: Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators. John Wiley, Sussex (2015)CrossRefzbMATHGoogle Scholar
  7. 7.
    Loève, M.: Probability Theory II. Springer, New York (1978)CrossRefzbMATHGoogle Scholar
  8. 8.
    Morris, J.S., Carroll, R.J.: Wavelet-based functional mixed models. J. R. Stat. Soc. Ser. B. 68 (2), 179–199 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Qin, L., Guo, W.: Functional mixed-effects model for periodic data. Biostatistics 7 (2), 225–234 (2006)CrossRefzbMATHGoogle Scholar
  10. 10.
    Satterthwaite, F.E.: Synthesis of variance. Psychometrika 6 (5), 309–316 (1941)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Shen, Q., Faraway, J.J.: An F test for linear models with functional responses. Stat. Sinica. 14 (4), 1239–1257 (2004)zbMATHMathSciNetGoogle Scholar
  12. 12.
    Zhang, J.T.: Analysis of Variance for Functional Data. CRC, New York (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Queen Mary University of LondonLondonUK
  2. 2.Otto-von-Guericke-University MagdeburgMagdeburgGermany

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