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Statistical Models for Data Analysis pp 161–169Cite as

A Metric Based Approach for the Least Square Regression of Multivariate Modal Symbolic Data

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Abstract

In this paper we propose a linear regression model for multivariate modal symbolic data. The observed variables are probabilistic modal variables according to the definition given in (Bock and Diday (2000). Analysis of symbolic data: exploratory methods for extracting statistical information from complex data. Springer), i.e. variables whose realizations are frequency or probability distributions. The parameters are estimated through a Least Squares method based on a suitable squared distance between the predicted and the observed modal symbolic data: the squared ℓ 2 Wasserstein distance. Measures of goodness of fit are also presented and an application on real data corroborates the proposed method.

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Notes

  1. 1.

    Note that if x is a vector of scalars Eq. (8) becomes \(\mathbf{{x}^{T}y} =\sum \limits _{ i=1}^{n}x_{i} \cdot \bar{ y}_{i}\).

  2. 2.

    http://java.epa.gov/castnet/.

  3. 3.

    We supply the full table of histogram data, the MatlabTM code and workspace upon request.

References

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Authors and Affiliations

  1. Dipartimento di Scienze Politiche “J. Monnet”, Seconda Universit degli Studi di Napoli, Caserta, Italy

    Antonio Irpino & Rosanna Verde

Authors
  1. Antonio Irpino
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  2. Rosanna Verde
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Corresponding author

Correspondence to Antonio Irpino .

Editor information

Editors and Affiliations

  1. Department of Economics, and Management, University of Pavia, Via San Felice 7, Pavia, 27100, Italy

    Paolo Giudici

  2. Department of Economics, and Business, University of Catania, Corso Italia 55, Catania, 95129, Italy

    Salvatore Ingrassia

  3. , Department of Statistics, University of Rome "La Sapienza", Piazzale Aldo Moro 5, Rome, 00185, Italy

    Maurizio Vichi

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Irpino, A., Verde, R. (2013). A Metric Based Approach for the Least Square Regression of Multivariate Modal Symbolic Data. In: Giudici, P., Ingrassia, S., Vichi, M. (eds) Statistical Models for Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00032-9_19

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