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A survey of functional principal component analysis

  • Han Lin Shang

    ()

Advances in data collection and storage have tremendously increased the presence of functional data, whose graphical representations are curves, images or shapes. As a new area of Statistics, functional data analysis extends existing methodologies and theories from the fields of functional analysis, generalized linear models, multivariate data analysis, nonparametric statistics and many others. This paper provides a review into functional data analysis with main emphasis on functional principal component analysis, functional principal component regression, and bootstrap in functional principal component regression. Recent trends as well as open problems in the area are discussed.

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2011/wp6-11.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 6/11.

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Length: 37 pages
Date of creation: May 2011
Date of revision:
Handle: RePEc:msh:ebswps:2011-6
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  1. Hervé Cardot, 2003. "Testing Hypotheses in the Functional Linear Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 241-255.
  2. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
  3. Ricardo Fraiman & Graciela Muniz, 2001. "Trimmed means for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 10(2), pages 419-440, December.
  4. John A. D. Aston & Jeng-Min Chiou & Jonathan P. Evans, 2010. "Linguistic pitch analysis using functional principal component mixed effect models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(2), pages 297-317.
  5. 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.
  6. Boente, Graciela & Rodriguez, Daniela & Sued, Mariela, 2010. "Inference under functional proportional and common principal component models," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 464-475, February.
  7. Besse, Philippe, 1992. "PCA stability and choice of dimensionality," Statistics & Probability Letters, Elsevier, vol. 13(5), pages 405-410, April.
  8. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501.
  9. Dauxois, J. & Pousse, A. & Romain, Y., 1982. "Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 136-154, March.
  10. D. S. Poskitt & Arivalzahan Sengarapillai, 2009. "Description Length and Dimensionality Reduction in Functional Data Analysis," Monash Econometrics and Business Statistics Working Papers 13/09, Monash University, Department of Econometrics and Business Statistics.
  11. Daniel Gervini, 2008. "Robust functional estimation using the median and spherical principal components," Biometrika, Biometrika Trust, vol. 95(3), pages 587-600.
  12. Hans-Georg Müller & Fang Yao, 2010. "Additive modelling of functional gradients," Biometrika, Biometrika Trust, vol. 97(4), pages 791-805.
  13. Yuko Araki & Sadanori Konishi & Shuichi Kawano & Hidetoshi Matsui, 2009. "Functional regression modeling via regularized Gaussian basis expansions," Annals of the Institute of Statistical Mathematics, Springer, vol. 61(4), pages 811-833, December.
  14. Ledyard Tucker, 1958. "Determination of parameters of a functional relation by factor analysis," Psychometrika, Springer, vol. 23(1), pages 19-23, March.
  15. Rob J. Hyndman & Han Lin Shang, 2008. "Rainbow plots, Bagplots and Boxplots for Functional Data," Monash Econometrics and Business Statistics Working Papers 9/08, Monash University, Department of Econometrics and Business Statistics.
  16. Mas, André, 2002. "Weak convergence for the covariance operators of a Hilbertian linear process," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 117-135, May.
  17. Herve Cardot & Robert Faivre & Michel Goulard, 2003. "Functional approaches for predicting land use with the temporal evolution of coarse resolution remote sensing data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(10), pages 1185-1199.
  18. Shang, Han Lin & Hyndman, Rob.J., 2011. "Nonparametric time series forecasting with dynamic updating," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1310-1324.
  19. López-Pintado, Sara & Romo, Juan, 2009. "On the Concept of Depth for Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 718-734.
  20. A. Delaigle & P. Hall & N. Bathia, 2012. "Componentwise classification and clustering of functional data," Biometrika, Biometrika Trust, vol. 99(2), pages 299-313.
  21. Tarpey, Thaddeus, 2007. "Linear Transformations and the k-Means Clustering Algorithm: Applications to Clustering Curves," The American Statistician, American Statistical Association, vol. 61, pages 34-40, February.
  22. Fengler, Matthias R. & Härdle, Wolfgang K. & Villa, Christophe, 2001. "The dynamics of implied volatilities: A common principal components approach," SFB 373 Discussion Papers 2001,38, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  23. Peter Hall & Mohammad Hosseini-Nasab, 2006. "On properties of functional principal components analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 109-126.
  24. Preda, C. & Saporta, G., 2005. "PLS regression on a stochastic process," Computational Statistics & Data Analysis, Elsevier, vol. 48(1), pages 149-158, January.
  25. Preda, C. & Saporta, G., 2005. "Clusterwise PLS regression on a stochastic process," Computational Statistics & Data Analysis, Elsevier, vol. 49(1), pages 99-108, April.
  26. Charles Bouveyron & Julien Jacques, 2011. "Model-based clustering of time series in group-specific functional subspaces," Advances in Data Analysis and Classification, Springer, vol. 5(4), pages 281-300, December.
  27. Antonio Cuevas & Manuel Febrero & Ricardo Fraiman, 2007. "Robust estimation and classification for functional data via projection-based depth notions," Computational Statistics, Springer, vol. 22(3), pages 481-496, September.
  28. Lopez-Pintado, Sara & Romo, Juan, 2007. "Depth-based inference for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4957-4968, June.
  29. Aurore Delaigle & Peter Hall, 2012. "Achieving near perfect classification for functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(2), pages 267-286, 03.
  30. Peter Hall & Céline Vial, 2006. "Assessing the finite dimensionality of functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 689-705.
  31. Cuevas, Antonio & Fraiman, Ricardo, 2009. "On depth measures and dual statistics. A methodology for dealing with general data," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 753-766, April.
  32. Müller, Hans-Georg & Yao, Fang, 2008. "Functional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1534-1544.
  33. Aneiros-Pérez, Germán & Vieu, Philippe, 2008. "Nonparametric time series prediction: A semi-functional partial linear modeling," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 834-857, May.
  34. Hlubinka, Daniel & Prchal, Lubos, 2007. "Changes in atmospheric radiation from the statistical point of view," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4926-4941, June.
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