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A fast and objective multidimensional kernel density estimation method: fastKDE

Author

Listed:
  • O’Brien, Travis A.
  • Kashinath, Karthik
  • Cavanaugh, Nicholas R.
  • Collins, William D.
  • O’Brien, John P.

Abstract

Numerous facets of scientific research implicitly or explicitly call for the estimation of probability densities. Histograms and kernel density estimates (KDEs) are two commonly used techniques for estimating such information, with the KDE generally providing a higher fidelity representation of the probability density function (PDF). Both methods require specification of either a bin width or a kernel bandwidth. While techniques exist for choosing the kernel bandwidth optimally and objectively, they are computationally intensive, since they require repeated calculation of the KDE. A solution for objectively and optimally choosing both the kernel shape and width has recently been developed by Bernacchia and Pigolotti (2011). While this solution theoretically applies to multidimensional KDEs, it has not been clear how to practically do so.

Suggested Citation

  • O’Brien, Travis A. & Kashinath, Karthik & Cavanaugh, Nicholas R. & Collins, William D. & O’Brien, John P., 2016. "A fast and objective multidimensional kernel density estimation method: fastKDE," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 148-160.
    • Handle: RePEc:eee:csdana:v:101:y:2016:i:c:p:148-160
    DOI: 10.1016/j.csda.2016.02.014
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    References listed on IDEAS

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    1. Ernst Wit & Edwin van den Heuvel & Jan-Willem Romeijn, 2012. "‘All models are wrong...’: an introduction to model uncertainty," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(3), pages 217-236, August.
    2. Tarn Duong & Martin L. Hazelton, 2005. "Cross‐validation Bandwidth Matrices for Multivariate Kernel Density Estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 485-506, September.
    3. Joerg Luedicke & Alberto Bernacchia, 2014. "Self-consistent density estimation," Stata Journal, StataCorp LLC, vol. 14(2), pages 237-258, June.
    4. Nils-Bastian Heidenreich & Anja Schindler & Stefan Sperlich, 2013. "Bandwidth selection for kernel density estimation: a review of fully automatic selectors," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 403-433, October.
    5. Alberto Bernacchia & Simone Pigolotti, 2011. "Self‐consistent method for density estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(3), pages 407-422, June.
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