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

Author

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  • İstem Köymen Keser
  • İpek Deveci Kocakoç
  • Ali Kemal Şehirlioğlu

Abstract

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.

Suggested Citation

  • İstem Köymen Keser & İpek Deveci Kocakoç & Ali Kemal Şehirlioğlu, 2016. "A New Descriptive Statistic for Functional Data: Functional Coefficient of Variation," Alphanumeric Journal, Bahadir Fatih Yildirim, vol. 4(2), pages 1-10, September.
    • Handle: RePEc:anm:alpnmr:v:4:y:2016:i:2:p:1-10
    DOI: http://dx.doi.org/10.17093/aj.2016.4.2.5000185408
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    References listed on IDEAS

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    1. J. Ramsay, 1982. "When the data are functions," Psychometrika, Springer;The Psychometric Society, vol. 47(4), pages 379-396, December.
    2. Coffey Norma & Hinde John, 2011. "Analyzing Time-Course Microarray Data Using Functional Data Analysis - A Review," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-32, May.
    3. Dennis D. Cox & Jong Soo Lee, 2008. "Pointwise testing with functional data using the Westfall--Young randomization method," Biometrika, Biometrika Trust, vol. 95(3), pages 621-634.
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    More about this item

    Keywords

    Coefficient of Variation Function; Descriptive Statistics; Functional Data Analysis;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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