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Dimensionality Reduction for Samples of Bivariate Density Level Sets: an Application to Electoral Results

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Recent Advances in Functional Data Analysis and Related Topics

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

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Abstract

A bivariate densities can be represented as a density level set containing a fixed amount of probability (0.75, for instance). Then a functional dataset where the observations are bivariate density functions can be analyzed as if the functional data are density level sets.We compute distances between sets and perform standard Multidimensional Scaling. This methodology is applied to analyze electoral results.

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References

  1. Borg, I., Groenen, P.: Modern Multidimensional Scaling: Theory and Applications (Second Edition). Springer Verlag, New York (2005).

    MATH  Google Scholar 

  2. Bowman, A. W., Azzalini, A.: Applied Smoothing Techniques for Data Analysis. Oxford University Press, Oxford (1997).

    MATH  Google Scholar 

  3. Cuevas, A., Fraiman, R.: Set estimation. In: Kendall, W., Molchanov, I. (eds.) New Perspectives in Stochastic Geometry. Oxford University Press, Oxford (2009).

    Google Scholar 

  4. Cuevas, A.: Set estimation: Another bridge between statistics and geometry. Bolet´ın de Estad ´ıtica e Investigaci´on Operativa 25 (2), 71–85 (2009).

    Google Scholar 

  5. Delicado, P.: Dimensionality reduction when data are density functions. Comput. Stat. Data Anal. 55 (1), 401–420 (2011).

    Article  Google Scholar 

  6. Jones, M.C., Rice, J.A.: Displaying the important features of large collections of similar curves. Amer. Statistician 46 (2), 140–145 (1992).

    Article  Google Scholar 

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Correspondence to Pedro Delicado .

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© 2011 Springer-Verlag Berlin Heidelberg

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Delicado, P. (2011). Dimensionality Reduction for Samples of Bivariate Density Level Sets: an Application to Electoral Results. In: Ferraty, F. (eds) Recent Advances in Functional Data Analysis and Related Topics. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2736-1_11

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