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Bagging of density estimators

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Abstract

In this work we give new density estimators by averaging classical density estimators such as the histogram, the frequency polygon and the kernel density estimators obtained over different bootstrap samples of the original data. Using existent results, we prove the \(L^2\)-consistency of these new estimators and compare them to several similar approaches by simulations. Based on them, we give also a way to construct non-parametric pointwise variability band for the target density.

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Acknowledgements

We would like to thank project ECOS-2014 Aprendizaje Automático para la Modelización y el Análisis de Recursos Naturales, no. U14E02, the LIA-IFUM and the ANII-Uruguay for their financial support.

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Authors and Affiliations

  1. IMERL, Facultad de Ingeniería, Universidad de la República, Montevideo, Uruguay

    Mathias Bourel

  2. DMC, Facultad de Ciencias Económicas y Administración, Universidad de la República, Montevideo, Uruguay

    Mathias Bourel

  3. Laboratoire ERIC EA 3083, Université Lumière Lyon 2, Lyon, France

    Jairo Cugliari

Authors
  1. Mathias Bourel
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  2. Jairo Cugliari
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Correspondence to Mathias Bourel.

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Appendix: Additional results

Appendix: Additional results

1.1 Quality of the estimation

For sake of completeness we present in this appendix the individual values of Fig. 3. In the following tables (Tables 3, 4, 5, 6, 7), values are \(100\times \)MISE obtained as mean average over 100 replicates. At each line, best results are shown in bold.

Table 3 MISE for sample size \(n=50\)
Full size table
Table 4 MISE for sample size \(n=100\)
Full size table
Table 5 MISE for sample size \(n=200\)
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Table 6 MISE for sample size \(n=500\)
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Table 7 MISE for sample size \(n=1000\)
Full size table

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Bourel, M., Cugliari, J. Bagging of density estimators. Comput Stat 34, 1849–1869 (2019). https://doi.org/10.1007/s00180-019-00889-9

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  • DOI: https://doi.org/10.1007/s00180-019-00889-9

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