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Description length and dimensionality reduction in functional data analysis

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  • Poskitt, D.S.
  • Sengarapillai, Arivalzahan

Abstract

The use of description length principles to select an appropriate number of basis functions for functional data is investigated. A flexible definition of the dimension of a random function that is constructed directly from the Karhunen–Loève expansion of the observed process or data generating mechanism is provided. The results obtained show that although the classical, principle component variance decomposition technique will behave in a coherent manner, in general, the dimension chosen by this technique will not be consistent in the conventional sense. Two description length criteria are described. Both of these criteria are proved to be consistent and it is shown that in low noise settings they will identify the true finite dimension of a signal that is embedded in noise. Two examples, one from mass spectroscopy and the other from climatology, are used to illustrate the basic ideas. The application of different forms of the bootstrap for functional data is also explored and used to demonstrate the workings of the theoretical results.

Suggested Citation

  • Poskitt, D.S. & Sengarapillai, Arivalzahan, 2013. "Description length and dimensionality reduction in functional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 98-113.
    • Handle: RePEc:eee:csdana:v:58:y:2013:i:c:p:98-113
    DOI: 10.1016/j.csda.2011.03.018
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    Cited by:

    1. Wong, Raymond K.W. & Zhang, Xiaoke, 2019. "Nonparametric operator-regularized covariance function estimation for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 131-144.
    2. Tengteng Xu & Riquan Zhang & Xiuzhen Zhang, 2023. "Estimation of spatial-functional based-line logit model for multivariate longitudinal data," Computational Statistics, Springer, vol. 38(1), pages 79-99, March.
    3. Jacques, Julien & Preda, Cristian, 2014. "Model-based clustering for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 92-106.
    4. Md Atikur Rahman Khan & D.S. Poskitt, 2010. "Description Length Based Signal Detection in singular Spectrum Analysis," Monash Econometrics and Business Statistics Working Papers 13/10, Monash University, Department of Econometrics and Business Statistics.
    5. Han Shang, 2014. "A survey of functional principal component analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 121-142, April.

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    More about this item

    Keywords

    Bootstrap; Consistency; Dimension determination; Karhunen–Loève expansion; Signal-to-noise ratio; Variance decomposition;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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