×

A comparison of tests for the one-way ANOVA problem for functional data. (English) Zbl 1329.65028

Summary: In this paper, some new tests based on the idea of the B-spline test [Q. Shen and J. Faraway, Stat. Sin. 14, No. 4, 1239–1257 (2004; Zbl 1060.62075)] for the one-way ANOVA problem for functional data are proposed. Eleven existing tests for this problem are also reviewed. Exhaustive simulation studies are presented to compare all of the tests considered. The simulations are based on real labeled times series data and artificial data. They provide an idea of the size control and power of the tests, and emphasize the differences between them. Illustrative examples of the use of the tests in practice are also given.

MSC:

62-08 Computational methods for problems pertaining to statistics
62J10 Analysis of variance and covariance (ANOVA)
62F03 Parametric hypothesis testing

Citations:

Zbl 1060.62075

Software:

fda (R)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] 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 · Zbl 1071.62037 · doi:10.1142/S0219691304000639
[2] Anderson TW (2003) An introduction to multivariate statistical analysis, 3rd edn. Wiley, London · Zbl 1039.62044
[3] Benhenni K, Ferraty F, Rachdi M, Vieu P (2007) Local smoothing regression with functional data. Comput Stat 22:353-369 · Zbl 1194.62042 · doi:10.1007/s00180-007-0045-0
[4] Berrendero JR, Justel A, Svarc M (2011) Principal components for multivariate functional data. Comput Stat Data Anal 55:2619-2634 · Zbl 1464.62025 · doi:10.1016/j.csda.2011.03.011
[5] Bobelyn E, Serban AS, Nicu M, Lammertyn J, Nicolai BM, Saeys W (2010) Postharvest quality of apple predicted by NIR-spectroscopy: study of the effect of biological variability on spectra and model performance. Postharvest Biol Technol 55:133-143 · doi:10.1016/j.postharvbio.2009.09.006
[6] Boente G, Fraiman R (2000) Kernel-based functional principal components. Ann Stat 20:655-674 · Zbl 0997.62024
[7] Cai T, Hall P (2006) Prediction in functional linear regression. Ann Stat 34:2159-2179 · Zbl 1106.62036 · doi:10.1214/009053606000000830
[8] Chiou JM, Müller HG (2007) Diagnostics for functional regression via residual processes. Comput Stat Data Anal 15:4849-4863 · Zbl 1162.62394 · doi:10.1016/j.csda.2006.07.042
[9] Cuevas A (2014) A partial overview of the theory of statistics with functional data. J Stat Plan Inference 147:1-23 · Zbl 1278.62012 · doi:10.1016/j.jspi.2013.04.002
[10] Cuevas A, Febrero M, Fraiman R (2002) Linear functional regression: the case of fixed design and functional response. Can J Stat 30:285-300 · Zbl 1012.62039 · doi:10.2307/3315952
[11] Cuevas A, Febrero M, Fraiman R (2004) An anova test for functional data. Comput Stat Data Anal 47:111-122 · Zbl 1429.62726 · doi:10.1016/j.csda.2003.10.021
[12] Davidian M, Lin X, Wang J (2004) Introduction: emerging issues in longitudinal and functional data analysis. Stat Sin 14:613-614
[13] Demšar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1-30 · Zbl 1222.68184
[14] Fan J, Lin SK (1998) Test of significance when data are curves. J Am Stat Assoc 93:1007-1021 · Zbl 1064.62525 · doi:10.1080/01621459.1998.10473763
[15] Faraway J (1997) Regression analysis for a functional response. Technometrics 39:254-261 · Zbl 0891.62027 · doi:10.1080/00401706.1997.10485118
[16] Ferraty F, Vieu P (2006) Nonparametric functional data analysis: theory and practice. Springer, New York · Zbl 1119.62046
[17] Gao HO (2007) Day of week effects on diurnal ozone/NOx cycles and transportation emissions in Southern California. Transp Res Part D 12:292-305 · doi:10.1016/j.trd.2007.03.004
[18] Górecki T, Krzyśko M, Waszak Ł (2014) Functional discriminant coordinates. Commun Stat Theory Methods 43:1013-1025 · Zbl 1462.62384 · doi:10.1080/03610926.2013.828074
[19] Hollander M, Wolfe DA (1973) Nonparametric statistical methods. Wiley, New York · Zbl 0277.62030
[20] Horváth L, Kokoszka P (2012) Inference for functional data with applications. Springer, New York · Zbl 1279.62017 · doi:10.1007/978-1-4614-3655-3
[21] Iman RL, Davenport JM (1980) Approximations of the critical region of the Friedman statistic. Commun. Stat. Theory Methods 9:571-595 · Zbl 0451.62061 · doi:10.1080/03610928008827904
[22] James GM, Hastie TJ (2001) Functional linear discriminant analysis for irregularly sampled curves. J R Stat Soc Ser B (Stat Methodol) 63:533-550 · Zbl 0989.62036 · doi:10.1111/1467-9868.00297
[23] Keogh E, Zhu Q, Hu B, Hao Y, Xi X, Wei L, Ratanamahatana CA (2011) The UCR Time Series Classification/Clustering Homepage. http://www.cs.ucr.edu/ eamonn/time_series_data/ · Zbl 1222.68184
[24] Krzyśko M, Waszak Ł (2013) Canonical correlation analysis for functional data. Biometr Lett 50:95-105
[25] Laukaitis A, Račkauskas A (2005) Functional data analysis for clients segmentation tasks. Eur J Oper Res 163:210-216 · Zbl 1067.90118 · doi:10.1016/j.ejor.2004.01.010
[26] Leurgans SE, Moyeed RA, Silverman BW (1993) Canonical correlation analysis when the data are curves. J R Stat Soc Ser B (Stat Methodol) 55:725-740 · Zbl 0803.62049
[27] Long W, Li N, Wang H, Cheng S (2012) Impact of US financial crisis on different countries: based on the method of functional analysis of variance. Procedia Comput Sci 9:1292-1298 · doi:10.1016/j.procs.2012.04.141
[28] Looney SW (1998) A statistical technique for comparing the accuracies of several classifiers. Pattern Recogn Lett 8:5-9 · Zbl 0709.62529 · doi:10.1016/0167-8655(88)90016-5
[29] Martínez-Camblor P, Corral N (2011) Repeated measures analysis for functional data. Comput Stat Data Anal 55:3244-3256 · Zbl 1261.65013 · doi:10.1016/j.csda.2011.06.007
[30] Nemenyi PB (1963) Distribution-free multiple comparisons. Dissertation, Princeton University
[31] Preda C, Saporta G, Lévéder C (2007) PLS classification of functional data. Comput Stat 22:223-235 · Zbl 1196.62086 · doi:10.1007/s00180-007-0041-4
[32] Ramsay JO, Hooker G, Graves S (2009) Functional data analysis with R and MATLAB. Springer, Berlin · Zbl 1179.62006 · doi:10.1007/978-0-387-98185-7
[33] Ramsay JO, Silverman BW (2002) Applied functional data analysis: methods and case studies. Springer, New York · Zbl 1011.62002 · doi:10.1007/b98886
[34] Ramsay JO, Silverman BW (2005) Functional data analysis, 2nd edn. Springer, New York · Zbl 1079.62006
[35] Shen Q, Faraway J (2004) An F test for linear models with functional responses. Stat Sin 14:1239-1257 · Zbl 1060.62075
[36] Tarrío-Saavedra J, Naya S, Francisco-Fernández M, Artiaga R, Lopez-Beceiro J (2011) Application of functional ANOVA to the study of thermal stability of micronano silica epoxy composites. Chemometr Intell Lab Syst 105:114-124 · doi:10.1016/j.chemolab.2010.11.006
[37] Tokushige S, Yadohisa H, Inada K (2007) Crisp and fuzzy \[k\] k-means clustering algorithms for multivariate functional data. Comput Stat 22:1-16 · Zbl 1196.62089 · doi:10.1007/s00180-006-0013-0
[38] Valderrama MJ (2007) An overview to modelling functional data. Comput Stat 22:331-334 · doi:10.1007/s00180-007-0043-2
[39] Yamamoto M, Terada Y (2014) Functional factorial \[KK\]-means analysis. Comput Stat Data Anal 79:133-148 · Zbl 1506.62200 · doi:10.1016/j.csda.2014.05.010
[40] Zhang JT (2011) Statistical inferences for linear models with functional responses. Stat Sin 21:1431-1451 · Zbl 1236.62081 · doi:10.5705/ss.2009.302
[41] Zhang JT (2013) Analysis of variance for functional data. Chapman & Hall, London
[42] Zhang JT, Chen JW (2007) Statistical inferences for functional data. Ann Stat 35:1052-1079 · Zbl 1129.62029 · doi:10.1214/009053606000001505
[43] Zhang JT, Liang X (2014) One-way ANOVA for functional data via globalizing the pointwise \[FF\]-test. Scand J Stat 41:51-71 · Zbl 1349.62331 · doi:10.1111/sjos.12025
[44] Zhao X, Marron JS, Wells MT (2004) The functional data analysis view of longitudinal data. Stat Sin 14:789-808 · Zbl 1073.62001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.