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Rainbow plots, Bagplots and Boxplots for Functional Data

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Author Info

  • Rob J. Hyndman

    ()

  • Han Lin Shang

    ()

Abstract

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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Bibliographic Info

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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Web page: http://www.buseco.monash.edu.au/depts/ebs/
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Web: http://www.buseco.monash.edu.au/depts/ebs/pubs/wpapers/

Related research

Keywords: Highest density regions; Robust principal component analysis; Kernel density estimation; Outlier detection; Tukey's halfspace depth;

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References

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  1. 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.
  2. Rob J. Hyndman & Md. Shahid Ullah, 2005. "Robust forecasting of mortality and fertility rates: a functional data approach," Monash Econometrics and Business Statistics Working Papers 2/05, Monash University, Department of Econometrics and Business Statistics.
  3. 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.
  4. V. Kargin & Alexei Onatski, 2004. "Curve Forecasting by Functional Autoregression," Discussion Papers 0405-18, Columbia University, Department of Economics.
  5. 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.
  6. 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.
  7. 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.
  8. Filzmoser, Peter & Maronna, Ricardo & Werner, Mark, 2008. "Outlier identification in high dimensions," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1694-1711, January.
  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. 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.
  11. 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.
  12. 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.
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Citations

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Cited by:
  1. Farah Yasmeen & Rob J Hyndman & Bircan Erbas, 2010. "Forecasting age-related changes in breast cancer mortality among white and black US women: A functional approach," Monash Econometrics and Business Statistics Working Papers 9/10, Monash University, Department of Econometrics and Business Statistics.
  2. Rob J Hyndman & Heather Booth & Farah Yasmeen, 2011. "Coherent mortality forecasting: the product-ratio method with functional time series models," Monash Econometrics and Business Statistics Working Papers 1/11, Monash University, Department of Econometrics and Business Statistics.
  3. Montes, Francisco & Sala, Ramón, 2012. "Equilibrio competitivo en Liga española de futbol de Primera División: Un test de Montecarlo basado en datos funcionales/Competitive Balance in the First Division Spanish Soccer League: A Montecarlo," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 30, pages 513-526, Agosto.

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