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Preprocessing of centred logratio transformed density functions using smoothing splines

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  • J. Machalová
  • K. Hron
  • G.S. Monti

Abstract

With large-scale database systems, statistical analysis of data, occurring in the form of probability distributions, becomes an important task in explorative data analysis. Nevertheless, due to specific properties of density functions, their proper statistical treatment of these data still represents a challenging task in functional data analysis. Namely, the usual metric does not fully accounts for the relative character of information, carried by density functions; instead, their geometrical features are captured by Bayes spaces of measures. The easiest possibility of expressing density functions in an space is to use centred logratio transformation, even though this results in functional data with a constant integral constraint that needs to be taken into account in further analysis. While theoretical background for reasonable analysis of density functions is already provided comprehensively by Bayes spaces themselves, preprocessing issues still need to be developed. The aim of this paper is to introduce optimal smoothing splines for centred logratio transformed density functions that take all their specific features into account and provide a concise methodology for reasonable preprocessing of raw (discretized) distributional observations. Theoretical developments are illustrated with a real-world data set from official statistics and with a simulation study.

Suggested Citation

  • J. Machalová & K. Hron & G.S. Monti, 2016. "Preprocessing of centred logratio transformed density functions using smoothing splines," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(8), pages 1419-1435, June.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:8:p:1419-1435
    DOI: 10.1080/02664763.2015.1103706
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    References listed on IDEAS

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    1. Delicado, P., 2011. "Dimensionality reduction when data are density functions," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 401-420, January.
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    Cited by:

    1. Dominique Guegan & Matteo Iacopini, 2018. "Nonparametric forecasting of multivariate probability density functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01821815, HAL.
    2. Karel Hron & Jitka Machalová & Alessandra Menafoglio, 2023. "Bivariate densities in Bayes spaces: orthogonal decomposition and spline representation," Statistical Papers, Springer, vol. 64(5), pages 1629-1667, October.
    3. Jitka Machalová & Renáta Talská & Karel Hron & Aleš Gába, 2021. "Compositional splines for representation of density functions," Computational Statistics, Springer, vol. 36(2), pages 1031-1064, June.
    4. Dominique Guégan & Matteo Iacopini, 2018. "Nonparameteric forecasting of multivariate probability density functions," Documents de travail du Centre d'Economie de la Sorbonne 18012, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Thomas-Agnan, Christine & Simioni, Michel & Trinh, Thi-Huong, 2023. "Discrete and Smooth Scalar-on-Density Compositional Regression for Assessing the Impact of Climate Change on Rice Yield in Vietnam," TSE Working Papers 23-1410, Toulouse School of Economics (TSE), revised Apr 2024.
    6. Matteo Iacopini & Dominique Guégan, 2018. "Nonparametric Forecasting of Multivariate Probability Density Functions," Working Papers 2018:15, Department of Economics, University of Venice "Ca' Foscari".
    7. Thomas-Agnan, Christine & Mondon, Camille & Trinh, Thi-Huong & Ruiz-Gazen, Anne, 2024. "ICS for complex data with application to outlier detection for density data objects," TSE Working Papers 24_1585, Toulouse School of Economics (TSE).
    8. Dominique Guegan & Matteo Iacopini, 2018. "Nonparametric forecasting of multivariate probability density functions," Post-Print halshs-01821815, HAL.
    9. Talská, R. & Menafoglio, A. & Machalová, J. & Hron, K. & Fišerová, E., 2018. "Compositional regression with functional response," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 66-85.

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