A Kendall correlation coefficient between functional data
Tóm tắt
Measuring dependence is a very important tool to analyze pairs of functional data. The coefficients currently available to quantify association between two sets of curves show a non robust behavior under the presence of outliers. We propose a new robust numerical measure of association for bivariate functional data. We extend in this paper Kendall coefficient for finite dimensional observations to the functional setting. We also study its statistical properties. An extensive simulation study shows the good behavior of this new measure for different types of functional data. Moreover, we apply it to establish association for real data, including microarrays time series in genetics.
Tài liệu tham khảo
Borovskikh Y (1996) U-statistics in Banach space. VSP BV, Oud-Beijerland
Cardot H, Ferraty F, Sarda P (1999) Functional linear model. Stat Probab Lett 45:11–22
Cuevas A, Febrero M, Fraiman R (2004) An ANOVA test for functional data. Comput Stat Data Anal 47:111–122
Delicado P (2007) Functional k-sample problem when data are density functions. Comput Stat 22:391–410
Dubin JA, Müller HG (2005) Dynamical correlation for multivariate longitudinal data. J Am Stat Assoc 100:872–881
Efron B (2004) Large-scale simultaneous hypothesis testing: the choice of a null hypothesis. J Am Stat Assoc 99:96–104
Efron B (2005) Local false discovery rates. Technical report, Department of Statistics, Stanford University
Escabias M, Aguilera A, Valderrama M (2004) Principal components estimation of functional logistic regression: discussion of two different approaches. J Non Parametr Stat 16(3–4):365–384
Febrero M, Galeano P, González-Manteiga W (2008) Outlier detection in functional data by depth measures, with application to identify abnormal \(NO_x\) levels. Envirometrics 19:331–345
He G, Müller HG, Wang JL (2000) Extending correlation and regression from multivariate to functional data. In: Puri ML (ed) Asymptotics in statistics and probability. VSP, Leiden, pp 197–210
Kendall M (1938) A new measure of rank correlation. Biometrika Trust 30(1/2):81–93
Leurgans SE, Moyeed RA, Silverman BW (1993) Canonical correlation analysis when data are curves. J R Stat Soc B 55:725–740
López-Pintado S, Romo J (2007) Depth-based inference for functional data. Comput Stat Data Anal 51:4957–4968
López-Pintado S, Romo J (2009) On the concept of depth for functional data. J Am Stat Assoc 104:718–734
Opgen-Rhein R, Strimmer K (2006) Inferring gene dependency networks from genomic longitudinal data: a functional data approach. REVSTAT 4(1):53–65
Pezulli S, Silverman B (1993) Some properties of smoothed components analysis for functional data. Comput Stat 8:1–16
Ramsay JO, Silverman BW (2005) Functional data analysis, 2nd edn. Springer, New York
Rangel C, Angus J, Ghahramani Z et al (2004) Modelling T-cell activation using gene expression profiling and state-space models. Bioinformatics 20:1361–1372
Scarsini M (1984) On measure of concordance. Stochastica 8(3):201–218
Schwabik S, Guoju Y (2005) Topics in Banach space integration. World Scientific Publishing, Singapore
Taylor MD (2007) Multivariate measures of concordance. Ann Inst Stat Math 59:789–806
Taylor MD (2008) Some properties of multivariate measures of concordance. arXiv:0808.3105 [math.PR]
Whittaker J (1990) Graphical models in applied multivariate statistics. Wiley, New York