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Convergence rates for unconstrained bandwidth matrix selectors in multivariate kernel density estimation

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  • Duong, Tarn
  • Hazelton, Martin L.

Abstract

Progress in selection of smoothing parameters for kernel density estimation has been much slower in the multivariate than univariate setting. Within the context of multivariate density estimation attention has focused on diagonal bandwidth matrices. However, there is evidence to suggest that the use of full (or unconstrained) bandwidth matrices can be beneficial. This paper presents some results in the asymptotic analysis of data-driven selectors of full bandwidth matrices. In particular, we give relative rates of convergence for plug-in selectors and a biased cross-validation selector.

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  • Duong, Tarn & Hazelton, Martin L., 2005. "Convergence rates for unconstrained bandwidth matrix selectors in multivariate kernel density estimation," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 417-433, April.
    • Handle: RePEc:eee:jmvana:v:93:y:2005:i:2:p:417-433
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    1. Jones, M. C. & Sheather, S. J., 1991. "Using non-stochastic terms to advantage in kernel-based estimation of integrated squared density derivatives," Statistics & Probability Letters, Elsevier, vol. 11(6), pages 511-514, June.
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    2. Madeleine Cule & Richard Samworth & Michael Stewart, 2010. "Maximum likelihood estimation of a multi‐dimensional log‐concave density," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 545-607, November.
    3. Martin L. Hazelton & Tilman M. Davies, 2022. "Pointwise comparison of two multivariate density functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1791-1810, December.
    4. Tiee-Jian Wu & Chih-Yuan Hsu & Huang-Yu Chen & Hui-Chun Yu, 2014. "Root $$n$$ n estimates of vectors of integrated density partial derivative functionals," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 865-895, October.
    5. Perrin, G. & Soize, C. & Ouhbi, N., 2018. "Data-driven kernel representations for sampling with an unknown block dependence structure under correlation constraints," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 139-154.
    6. Gramacki, Artur & Gramacki, Jarosław, 2017. "FFT-based fast bandwidth selector for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 27-45.
    7. Sobom M. Somé & Célestin C. Kokonendji & Smail Adjabi & Naushad A. Mamode Khan & Said Beddek, 2024. "Multiple combined gamma kernel estimations for nonnegative data with Bayesian adaptive bandwidths," Computational Statistics, Springer, vol. 39(2), pages 905-937, April.
    8. 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.
    9. Gery Geenens & Arthur Charpentier & Davy Paindaveine, 2014. "Probit Transformation for Nonparametric Kernel Estimation of the Copula Density," Working Papers ECARES ECARES 2014-23, ULB -- Universite Libre de Bruxelles.

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