Rainbow plots, bagplots, and boxplots for functional data

Journal of Computational and Graphical Statistics

Volumn 19, Issue 1, 2010, Pages 29-45

  Hyndman, Rob J ^a   Shang, Han Lin ^a  

^a MONASH UNIVERSITY   (Australia)

Author keywords

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

Indexed keywords

EID: 77749302275     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/jcgs.2009.08158     Document Type: Article

References (39)

1. Becker, C., and Gather, U. (2001), "The Largest Nonidentifiable Outlier: A Comparison of Multivariate Simultaneous Outlier Identification Rules," Computational Statistics & Data Analysis, 36 (1), 119-127. [39]
2. Croux, C., and Ruiz-Gazen, A. (2005), "High Breakdown Estimators for Principal Components: The ProjectionPursuit Approach Revisited," Journal of Multivariate Analysis, 95 (1), 206-226. [33]
3. Dioses, T., Dávalos, R., and Zuzunaga, J. (2002), "El Niño 1982-1983 and 1997-1998: Effects on Peruvian Jack Mackerel and Peruvian Chub Mackerel," Investigaciones Marinas, 30 (1), 185-187. [35]
4. Duong, T., and Hazelton, M. L. (2005), "Cross-Validation Bandwidth Matrices for Multivariate Kernel Density Estimation," Scandinavian Journal of Statistics, 32 (3), 485-506. [37]
5. Epifanio, I. (2008), "Shape Descriptors for Classification of Functional Data," Technometrics, 50 (3), 284-294. [43]
6. Eubank, R. L. (1999), Nonparametric Regression and Spline Smoothing (2nd ed.), New York: CRC. [32]
7. Faber, N. M., Song, X.-H., and Hopke, P. K. (2003), "Sample-Specific Standard Error of Prediction for Partial Least Squares Regression," TrAC Trends in Analytical Chemistry, 22 (5), 330-334. [43]
8. Febrero, M., Galeano, P., and Gonzalez-Manteiga, W. (2007), "A Functional Analysis of NOx Levels: Location and Scale Estimation and Outlier Detection," Computational Statistics, 22 (3), 411-427. [30,32,38]
9. Febrero, M., Galeano, P., and Gonzalez-Manteiga, W. (2008), "Outlier Detection in Functional Data by Depth Measures, With Application to Identify Abnormal NOx Levels," Environmetrics, 19 (4), 331-345. [30]
10. Ferraty, F., and Vieu, P. (2006), Nonparametric Functional Data Analysis: Theory and Practice, New York: Springer. [29,43]
11. Filzmoser, P. (2004), "A Multivariate Outlier Detection Method," in Proceedings of the Seventh International Conference on Computer Data Analysis and Modeling, Vol.1, eds. S. Aivazian, P. Filzmoser, and Y. Kharin, Minsk: Belarusian State University, pp. 18-22. [41]
12. Filzmoser, P., Maronna, R., and Werner, M. (2008), "Outlier Identification in High Dimensions," Computational Statistics & Data Analysis, 52 (3), 1694-1711. [39,40]
13. Gasser, T., Hall, P., and Presnell, B. (1998), "Nonparametric Estimation of the Mode of a Distribution of Random Curves," Journal of the Royal Statistical Society, Ser. B, 60 (4), 681-691. [43]
14. Hardin, J., and Rocke, D. M. (2005), "The Distribution of Robust Distances," Journal of Computational and Graphical Statistics, 14 (4), 928-946. [39]
15. Human Mortality Database (2009), University of California, Berkeley (USA) and Max Planck Institute for Demographic Research (Germany). Available at http://www.mortality.org/ (data downloaded on 15/4/2009). [30]
16. Hyde, V., Jank, W., and Shmueli, G. (2006), "Investigating Concurrency in Online Auctions Through Visualization," The American Statistician, 60 (3), 241-250. [30]
17. Hyndman, R. J. (1996), "Computing and Graphing Highest Density Regions," The American Statistician, 50 (2), 120-126. [31,32,36]
18. Hyndman, R. J., and Ullah, M. S. (2007), "Robust Forecasting ofMortality and Fertility Rates: A Functional Data Approach," Computational Statistics & Data Analysis, 51 (10), 4942-4956. [29,30,39]
19. Inselberg, A. (1985), "The Plane With Parallel Coordinates," The Visual Computer, 1 (2), 69-91. [32]
20. Jones, M. C., and Rice, J. A. (1992), "Displaying the Important Features of Large Collections of Similar Curves," The American Statistician, 46 (2), 140-145. [32,33]
21. Kargin, V., and Onatski, A. (2008), "Curve Forecasting by Functional Autoregression," Journal of Multivariate Analysis, 99 (10), 2508-2526. [29]
22. Locantore, N., Marron, J. S., Simpson, D. G., Tripoli, N., Zhang, J. T., and Cohen, K. L. (1999), "Robust Principal Component Analysis for Functional Data," Test, 8 (1), 1-73. [29]
23. López-Pintado, S., and Romo, J. (2009), "On the Concept of Depth for Functional Data," Journal of the American Statistical Association, 104 (486), 718-734. [33,41]
24. Moran, E. F., Adams, R., Bakoyéma, B., Stefano, F. T., and Boucek, B. (2006), "Human Strategies for Coping With El Niño Related Drought in Amazônia," Climatic Change, 77 (3-4), 343-361. [35]
25. Ramsay, J. O., and Ramsey, J. B. (2002), "Functional Data Analysis of the Dynamics of the Monthly Index of Nondurable Goods Production," Journal of Econometrics, 107 (1-2), 327-344. [30]
26. Ramsay, J. O., and Silverman, B. W. (2002), Applied Functional Data Analysis: Methods and Case Studies, New York: Springer. [29]
27. Ramsay, J. O., and Ramsey, J. B. (2005), Functional Data Analysis (2nd ed.), New York: Springer. [29,32]
28. Reiss, P. T., and Ogden, T. R. (2007), "Functional Principal Component Regression and Functional Partial Least Squares," Journal of the American Statistical Association, 102 (479), 984-996. [29]
29. Rocke, D. M. (1996), "Robustness Properties of S-Estimators of Multivariate Location and Shape in High Dimension," The Annals of Statistics, 24 (3), 1327-1345. [40]
30. Rousseeuw, P., Ruts, I., and Tukey, J. W. (1999), "The Bagplot: A Bivariate Boxplot," The American Statistician, 53 (4), 382-387. [31,34,35]
31. Scott, D.W. (1992), Multivariate Density Estimation: Theory, Practice, and Visualization, New York:Wiley. [31, 33]
32. Sood, A., James, G. M., and Tellis, G. J. (2009), "Functional Regression: A New Model for Predicting Market Penetration of New Products," Marketing Science, 28 (1), 36-51. [31,33]
33. Swayne, D. F., Cook, D., and Buja, A. (1998), "XGobi: Interactive Dynamic Data Visualization in the XWindow System," Journal of Computational and Graphical Statistics, 7 (1), 113-130. [43]
34. Timmermann, A., Oberhuber, J., Bacher, A., Esch, M., Latif, M., and Roeckner, E. (1999), "Increased El Niño Frequency in a Climate Model Forced by Future Greenhouse Warming,"Nature, 398 (6729), 694-697. [35]
35. Tukey, J. W. (1975), "Mathematics and the Picturing of Data," in Proceedings of the International Congress of Mathematicians, Vol.2, August 21-29, 1974, ed. R. D. James, Vancouver: Canadian Mathematical Society, pp. 523-531. [31-34,43]
36. Tukey, J. W. (1977), Exploratory Data Analysis, London: Addison-Wesley. [35]
37. Wegman, E. J. (1990), "Hyperdimensional Data Analysis Using Parallel Coordinates," Journal of the American Statistical Association, 85 (411), 664-675. [32]
38. Zhang, L., Marron, J. S., Shen, H., and Zhu, Z. (2007), "Singular Value Decomposition and Its Visualization," Journal of Computational and Graphical Statistics, 16 (4), 833-854. [30]
39. Adler, D., and Murdoch, D. (2009), "rgl: 3D Visualization Device System (OpenGL)," R package version 0.87, available at http://CRAN.R- project.org/package=rgl. [43]