New insights on permutation approach for hypothesis testing on functional data

Advances in Data Analysis and Classification

Volumn 8, Issue 3, 2014, Pages 339-356

  Corain, Livio ^a   Melas, Viatcheslav B ^b   Pepelyshev, Andrey ^b   Salmaso, Luigi ^a  

^a UNIVERSITY OF PADOVA   (Italy)

^b ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

Data compression; Functional data; Nonparametric combination; Permutation tests; Permutationally equivalent test statistic

Indexed keywords

DATA COMPRESSION; STATISTICAL TESTS;

FUNCTIONAL DATAS; HYPOTHESIS TESTING; NON-PARAMETRIC; NONPARAMETRIC INFERENCE; PERMUTATION APPROACH; PERMUTATION PROCEDURES; PERMUTATION TESTS; TEST STATISTICS;

POPULATION STATISTICS;

EID: 84907600492     PISSN: 18625347     EISSN: 18625355     Source Type: Journal    
DOI: 10.1007/s11634-013-0162-2     Document Type: Article

References (32)

1. Bai Z, Saranadasa H (1996) Effect of high dimension: by an example of a two sample problem. Statistica Sinica 6(2): 311-329.
2. Basso D, Pesarin F, Salmaso L, Solari A (2009) Permutation tests for Stochastic ordering and ANOVA: theory and applications with R. In: Lecture notes in Statistics, Springer, New York, USA.
3. Brunner E, Bathke A, Placzek M (2012) Estimation of box's ε for low- and high-dimensional repeated measures designs with unequal covariance matrices. Biometr J 54(3): 301-316.
4. Cao G, Yang L, Todem D (2012) Simultaneous inference for the mean function based on dense functional data. J Nonparametr Stat 24: 359-377.
5. Cardot H, Prchal L, Sarda P (2007) No effect and lack-of-fit permutation tests for functional regression. Comput Stat 22: 371-390.
6. Corain L, Melas V, Salmaso L, Pepelyshev A (2013) Optimal adaptive Fourier-Based testing for the equality of two nonparametric regression curves. Biometr J.
7. Cox D, Lee J (2008) Pointwise testing with functional data using the Westfall-Young randomization method. Biometrika 95: 621-634.
8. Cuevas A, Febrero M, Fraiman R (2004) An ANOVA test for functional data. Comput Stat Data Anal 47: 111-122.
9. Davidian M, Lin X, Wang J (2004) Introduction: emerging issues in longitudinal and functional data analysis. Stat Sinica 14: 613-614.
10. Diggle P, Heagerty P, Liang K-Y, Zeger S (2002) Analysis of longitudinal data. In: 2nd edn. Oxford University Press.
11. Edgington E, Onghena P (2007) Randomization tests, 4th edn. Chapman and Hall, London.
12. Fan J, Li S-K (1998) Test of significance when data are curves. J Am Stat Assoc 93: 1007-1021.
13. Ferraty F, Vieu P (2006) Nonparametric functional data analysis., Springer series in statistics Springer, New York.
14. Folks J (1984) Combinations of independent tests. In: Krishnaiah P, Sen P (eds) Handbook of statistics, vol 4. North-Holland, Amsterdam, pp 113-121.
15. Good P (2010) Permutation, parametric, and bootstrap tests of hypotheses, 3rd edn., Springer series in statistics Springer, New York.
16. Hall P, van Keilegom I (2007) Two-sample tests in functional data analysis starting from discrete data. Stat Sinica 17: 1511-1531.
17. Konietschke F, Pauly M (2013) Bootstrapping and permuting paired t-test type statistics. Stat Comput. doi: 10. 1007/s11222-012-9370-4.
18. Martinez-Camblor P, Corral N (2011) Repeated measures analysis for functional data. Comput Stat Data Anal 55: 3244-3256.
19. Mielke P, Berry K (2007) Permutation methods, a distance function approach, 2nd edn. Springer, New York.
20. Mohdeb Z, Mezhoud K, Boudaa D (2010) Testing the equality of nonparametric regression curves based on Fourier coefficients. J Afrika Stat 5: 219-227.
21. Munoz-Maldonado Y, Staniswalis J, Irwin L, Byers D (2002) A similarity analysis of curves. Can J Stat 30: 373-381.
22. Pesarin F, Salmaso L (2010) Permutation tests for complex data: theory. Applications and software, Wiley series in probability and statistics, Chichester, UK.
23. Ramsay J, Hooker G, Graves S (2009) Functional data analysis with R and Matlab. Springer, New York.
24. Ramsay J, Silverman B (2005) Functional data analysis, 2nd edn. Springer, New York.
25. Reboussin D, DeMets D (1996) Exact permutation inference for two sample repeated measures data. Commun Stat Theory Methods 25: 2223-2238.
26. Rice J (2004) Functional and longitudinal data analysis: perspectives on smoothing. Stat Sinica 14: 631-647.
27. Shen Q, Faraway J (2004) An F test for linear models with functional responses. Stat Sinica 14: 1239-1257.
28. Sirski M (2012) On the statistical analysis of functional data arising from designed experiments. Ph. D. Thesis, Department of Statistics, University of Manitoba.
29. Spitzner D (2008) A powerful test based on tapering for use in functional data analysis. Electron J Stat 2: 939-962.
30. Sturino J, Zorych I, Mallick B, Pokusaeva K, Chang Y-Y, Carroll R, Bliznuyk N (2010) Statistical methods for comparative phenomics using high-throughput phenotype microarrays. Int J Biostat 6.
31. Wang H, Akritas M (2011) Asymptotically distribution free tests in heteroscedastic unbalanced high dimensional anova. Stat Sinica 21: 1341-1377.
32. Zhang J-T, Chen J (2007) Statistical inferences for functional data. Annal Stat 35: 1052-1079.