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Full bandwidth matrix selectors for gradient kernel density estimate

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  • Horová, Ivana
  • Koláček, Jan
  • Vopatová, Kamila

Abstract

The most important factor in multivariate kernel density estimation is a choice of a bandwidth matrix. This choice is particularly important, because of its role in controlling both the amount and the direction of multivariate smoothing. Considerable attention has been paid to constrained parameterization of the bandwidth matrix such as a diagonal matrix or a pre-transformation of the data. A general multivariate kernel density derivative estimator has been investigated. Data-driven selectors of full bandwidth matrices for a density and its gradient are considered. The proposed method is based on an optimally balanced relation between the integrated variance and the integrated squared bias. The analysis of statistical properties shows the rationale of the proposed method. In order to compare this method with cross-validation and plug-in methods the relative rate of convergence is determined. The utility of the method is illustrated through a simulation study and real data applications.

Suggested Citation

  • Horová, Ivana & Koláček, Jan & Vopatová, Kamila, 2013. "Full bandwidth matrix selectors for gradient kernel density estimate," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 364-376.
    • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:364-376
    DOI: 10.1016/j.csda.2012.07.006
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    References listed on IDEAS

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    1. Zougab, Nabil & Adjabi, Smail & Kokonendji, Célestin C., 2014. "Bayesian estimation of adaptive bandwidth matrices in multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 28-38.

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