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Functional Data Analysis in Designed Experiments

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mODa 11 - Advances in Model-Oriented Design and Analysis

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

Abstract

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.

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References

  1. Antoniadis, A., Sapatinas, T.: Estimation and inference in functional mixed-effects models. Comput. Stat. Data Anal. 51 (10), 4793–4813 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bailey, R.A.: Design of Comparative Experiments. Cambridge University Press, Cambridge (2008)

    Book  MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  4. Faraway, J.J.: Regression analysis for a functional response. Technometrics 39 (3), 254–261 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  5. Guo, W.: Functional mixed effects models. Biometrics 58 (1), 121–128 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  6. Hsing, T., Eubank, R.: Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators. John Wiley, Sussex (2015)

    Book  MATH  Google Scholar 

  7. Loève, M.: Probability Theory II. Springer, New York (1978)

    Book  MATH  Google Scholar 

  8. Morris, J.S., Carroll, R.J.: Wavelet-based functional mixed models. J. R. Stat. Soc. Ser. B. 68 (2), 179–199 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  9. Qin, L., Guo, W.: Functional mixed-effects model for periodic data. Biostatistics 7 (2), 225–234 (2006)

    Article  MATH  Google Scholar 

  10. Satterthwaite, F.E.: Synthesis of variance. Psychometrika 6 (5), 309–316 (1941)

    Article  MATH  MathSciNet  Google Scholar 

  11. Shen, Q., Faraway, J.J.: An F test for linear models with functional responses. Stat. Sinica. 14 (4), 1239–1257 (2004)

    MATH  MathSciNet  Google Scholar 

  12. Zhang, J.T.: Analysis of Variance for Functional Data. CRC, New York (2013)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Queen Mary University of London, London, UK

    Bairu Zhang

  2. Otto-von-Guericke-University Magdeburg, Magdeburg, Germany

    Heiko Großmann

Authors
  1. Bairu Zhang
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  2. Heiko Großmann
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Corresponding author

Correspondence to Bairu Zhang .

Editor information

Editors and Affiliations

  1. Department of Statistics, Technische Universität Dortmund, Dortmund, Germany

    Joachim Kunert

  2. Department of Statistics, Technische Universität Dortmund, Dortmund, Germany

    Christine H. Müller

  3. Department of Statistics, London School of Economics, London, United Kingdom

    Anthony C. Atkinson

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© 2016 Springer International Publishing Switzerland

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Zhang, B., Großmann, H. (2016). Functional Data Analysis in Designed Experiments. In: Kunert, J., Müller, C., Atkinson, A. (eds) mODa 11 - Advances in Model-Oriented Design and Analysis. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-31266-8_27

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