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
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Note that if x is a vector of scalars Eq. (8) becomes \(\mathbf{{x}^{T}y} =\sum \limits _{ i=1}^{n}x_{i} \cdot \bar{ y}_{i}\).
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- 3.
We supply the full table of histogram data, the MatlabTM code and workspace upon request.
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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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DOI: https://doi.org/10.1007/978-3-319-00032-9_19
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