A New Descriptive Statistic for Functional Data: Functional Coefficient Of Variation

985 315


In this study, we propose a new descriptive statistic, coefficient of variation function, for functional data analysis and present its utilization. We recommend coefficient of variation function, especially when we want to compare the variation of multiple curve groups and when the mean functions are different for each curve group. Besides, obtaining coefficient of variation functions in terms of cubic B-Splines enables the interpretation of the first and second derivative functions of these functions and provides a stronger inference for the original curves. The utilization and effects of the proposed statistic is reported on a well-known data set from the literature. The results show that the proposed statistic reflects the variability of the data properly and this reflection gets clearer than that of the standard deviation function especially as mean functions differ.  

Full Text:

Article in press

DOI: http://dx.doi.org/10.17093/aj.2016.4.2.5000185408


Clarkson, D.B., Fraley, C., Gu, C., Ramsay, J.(2005). S+Functional Data Analysis User's Manual for Windows ®, Springer-Verlag, New-York.

Coffey, N., Hinde, J.(2011). Analyzing time-course microarray data using functional data analysis-a review. Statistical Applications in Genetics and Molecular Biology, 10(1),1-32.

Cox, D.D., and Lee, J.S. (2008). Pointwise testing with functional data using the Westfall-Young randomization method, Biometrika, 95(3), 621-634.

Keser, I.K. (2014). “Comparing two mean humidity curves using functional t-tests: Turkey case”, Electronic Journal of Applied Statistical Analysis, 7(2), 254-278.

Keser, I.K, Deveci Kocakoç, I. (2015), FDAPackage, software. Available at http://people.deu.edu.tr/istem.koymen/fda.html.

Lee, J.S. (2005). Aspects of Functional Data Inference and Its Applications. Doctor of Philosophy, Houston, Texas.

Levitin, D.J., Nuzzo, R.L., Vines Bradley W., Ramsay J.O., (2007). Introduction to Functional Data Analysis, Canadian Psychology, 48(3), 135-155.

Ramsay, J.O. (1982). When the data are functions, Psychometrika 47, 379-396.

Ramsay, J.O. (2015). FDAPackage, software. Available at: http://www.psych.mcgill.ca/misc/fda/downloads/FDAfuns/Matlab/.

Ramsay, J.O., Hooker, G., Graves, S. (2009). Functional Data Analysis with R and MATLAB, Springer-Verlag, New-York.

Ramsay J.O, Silverman B.W. (1997). Functional Data Analysis, Springer-Verlag, New-York.

Ramsay, J.O, Silverman, B.W. (2005). Functional Data Analysis, Second Edition, Springer-Verlag, New-York.

Rice, J. A., Silverman, B.W. (1991). Estimating the Mean and Covariance Structure When the Data are Curves, Journal of the Royal Statistical Society. Series B. 53(1), 233-243.

Shang, H.L. (2015). Resampling Techniques for Estimating the Distribution of Descriptive Statistics of Functional Data, Communications in Statistics - Simulation and Computation, 44:3, 614-635.

Sun, Y., Genton, M.G. (2011) Functional Boxplots, Journal of Computational and Graphical Statistics, 20:2, 316-334, DOI: 10.1198/jcgs.2011.09224

Tuddenham, R., Snyder, M. (1954). Physical growth of California boys and girls from birth to age 18. California Publications on Child Development, 1, 183-364.

Ullah, S., Finch, C. F. (2013). Applications of functional data analysis: a systematic review, BMC Medical Research Methodology, 13(43), 539–572.

Yaree, K. (2011). Functional data analysis with application to ms and cervical vertebrae data. Master of Science in Statistics, Edmonton, Alberta.

Zhang, J-T. (2013). Analysis of Variance for Functional Data, CRC Press.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.