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Rainbow plots, Bagplots and Boxplots for Functional Data

  • Rob J. Hyndman

    ()

  • Han Lin Shang

    ()

We propose new tools for visualizing large numbers of functional data in the form of smooth curves or surfaces. The proposed tools include functional versions of the bagplot and boxplot, and make use of the first two robust principal component scores, Tukey's data depth and highest density regions. By-products of our graphical displays are outlier detection methods for functional data. We compare these new outlier detection methods with exiting methods for detecting outliers in functional data and show that our methods are better able to identify the outliers.

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2008/wp9-08.pdf
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Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 9/08.

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Length: 26 pages
Date of creation: Nov 2008
Date of revision:
Handle: RePEc:msh:ebswps:2008-9
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  1. Ramsay, James O. & Ramsey, James B., 2002. "Functional data analysis of the dynamics of the monthly index of nondurable goods production," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 327-344, March.
  2. Manuel Febrero & Pedro Galeano & Wenceslao González-Manteiga, 2007. "A functional analysis of NOx levels: location and scale estimation and outlier detection," Computational Statistics, Springer, vol. 22(3), pages 411-427, September.
  3. Kargin, V. & Onatski, A., 2008. "Curve forecasting by functional autoregression," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2508-2526, November.
  4. Reiss, Philip T. & Ogden, R. Todd, 2007. "Functional Principal Component Regression and Functional Partial Least Squares," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 984-996, September.
  5. Filzmoser, Peter & Maronna, Ricardo & Werner, Mark, 2008. "Outlier identification in high dimensions," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1694-1711, January.
  6. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
  7. Croux, Christophe & Ruiz-Gazen, Anne, 2005. "High breakdown estimators for principal components: the projection-pursuit approach revisited," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 206-226, July.
  8. Tarn Duong & Martin L. Hazelton, 2005. "Cross-validation Bandwidth Matrices for Multivariate Kernel Density Estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 485-506.
  9. Hyde, Valerie & Jank, Wolfgang & Shmueli, Galit, 2006. "Investigating Concurrency in Online Auctions Through Visualization," The American Statistician, American Statistical Association, vol. 60, pages 241-250, August.
  10. Sara Lopez-Pintado & Juan Romo, 2006. "On The Concept Of Depth For Functional Data," Statistics and Econometrics Working Papers ws063012, Universidad Carlos III, Departamento de Estadística y Econometría.
  11. Becker, Claudia & Gather, Ursula, 2001. "The largest nonidentifiable outlier: a comparison of multivariate simultaneous outlier identification rules," Computational Statistics & Data Analysis, Elsevier, vol. 36(1), pages 119-127, March.
  12. Struyf, Anja & Rousseeuw, Peter J., 2000. "High-dimensional computation of the deepest location," Computational Statistics & Data Analysis, Elsevier, vol. 34(4), pages 415-426, October.
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