A simple multiway ANOVA for functional data

Test

Volumn 19, Issue 3, 2010, Pages 537-557

  Cuesta Albertos, J A ^a   Febrero Bande, M ^b  

^a UNIVERSITY OF CANTABRIA   (Spain)

^b UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

ANOVA; Functional data; Random projections; Testing; Two way ANOVA

Indexed keywords

EID: 78449251512     PISSN: 11330686     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11749-010-0185-3     Document Type: Article

References (30)

1. Abramovich F, Angelini C (2005) Testing in mixed-effects FANOVA models. J Stat Plan Inference 136: 4326-4348.
2. Abramovich F, Antoniadis A, Sapatinas T, Vidakovic B (2004) Optimal testing in a fixed-effects functional analysis of variance model. Int J Wavelets Multiresolut Inf Process 2: 323-349.
3. Angelini C, Vidakovic B (2002) Some novel methods in wavelet data analysis: Wavelet ANOVA, F-test shrinkage and Γ-minimax wavelet shrinkage. Istituto per le Applicazioni del Calcolo "Mauro Picone." Rapporti Tecnici RT 256/02.
4. Antoniadis A, Sapatinas T (2007) Estimation and inference in functional mixed-effects models. Comput Stat Data Anal 51: 4793-4813.
5. Benjamini Y, Hochberg Y (1995) Controlling the false discovery rate: a practical and powerful approach to multiple testing. J R Stat Soc Ser B 57: 289-300.
6. Benjamini Y, Yekutieli D (2001) The control of the false discovery rate in multiple testing under dependency. Ann Stat 29: 1165-1188.
7. Brumback BA, Rice JA (1998) Smoothing spline models for the analysis of nested and crossed samples of curves. J Am Stat Assoc 93: 961-994.
8. Brunner E, Dette H, Munk A (1997) Box-type approximations in nonparametric factorial designs. J Am Stat Assoc 92: 1494-1502.
9. Cuesta-Albertos JA, Nieto-Reyes A (2007) An infinite dimensional depth: The random Tukey depth. Technical Report.
10. Cuesta-Albertos JA, Nieto-Reyes A (2008) The random Tukey depth. Comput Stat Data Anal 52: 4979-4988.
11. Cuesta-Albertos JA, del Barrio T, Fraiman R, Matrán C (2007a) The random projection method in goodness of fit for functional data. Comput Stat Data Anal 51: 4814-4831.
12. Cuesta-Albertos JA, Fraiman R, Galves A, García J, Svarc M (2007b) Identifying rhythmic classes of languages using their sonority: a Kolmogorov-Smirnov approach. J Appl Stat 34: 749-761.
13. Cuesta-Albertos JA, Fraiman R, Ransford T (2007c) A sharp form of the Cramér-Wold theorem. J Theor Probab 20: 201-209.
14. Cuesta-Albertos JA, Cuevas A, Fraiman R (2008) On projection-based tests for spherical and compositional data. Stat Comput 19: 367-380.
15. Cuevas A, Fraiman R (2009) On depth measures and dual statistics. A methodology for dealing with general data. J Multivar Anal 100: 753-766.
16. Cuevas A, Febrero M, Fraiman R (2004) An ANOVA test for functional data. Comput Stat Data Anal 47: 111-122.
17. Fan J (1996) Tests of significance based on wavelet thresholding and Neyman's truncation. J Am Stat Assoc 91: 674-688.
18. Fan J, Lin SK (1998) Test of significance when data are curves. J Am Stat Assoc 93: 254-261.
19. Faraway JJ (1997) Regression analysis for a functional response. J R Stat Soc B 64: 887-898.
20. Ferraty F, Vieu P (2006) Nonparametric functional data analysis: theory and practice. Springer series in statistics. Springer, New York.
21. Ferraty F, Vieu P, Viguier-Pla S (2007) Factor-based comparison of groups of curves. Comput Stat Data Anal 51: 4903-4910.
22. Fujikoshi Y, Himeno T, Wakaki H (2004) Asymptotic results of a high dimensional MANOVA and power comparisons when the dimension is large compared to the sample size. J Jpn Stat Soc 34: 19-26.
23. Gu C (2002) Smoothing spline ANOVA models. Springer, New York.
24. Guo W (2002) Inference in smoothing spline analysis of variance. J R Stat Soc B 64: 887-898.
25. Krzanowski WJ (1988) Principles of multivariate analysis. A user's perspective. Oxford University Press, Oxford.
26. R Development Core Team (2007) R: a language and environment for statistical computing, Vienna, Austria. ISBN 3-900051-07-0, http://www. R-project. org.
27. Ramsay JO, Silverman BW (2002) Applied functional data analysis. Methods and case studies. Springer, New York.
28. Ramsay JO, Silverman BW (2005) Functional data analysis, 2nd edn. Springer, New York.
29. Schott JR (2007) Some high-dimensional tests for a one-way ANOVA. J Multivar Anal 98: 1825-1839.
30. Shohat JA, Tamarkin JD (1963) The problem of moments. American Mathematical Society, Providence.