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One-sided cross-validation for nonsmooth density functions

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  • Olga Y. Savchuk

    (University of South Florida)

Abstract

One-sided cross-validation (OSCV) is a bandwidth selection method initially introduced by Hart and Yi (J Am Stat Assoc 93(442):620–631, 1998) in the context of smooth regression functions. Martínez-Miranda et al. (in Gregoriou (ed) Operational risk towards basel III: best practices and issues in modeling, management and regulation, Wiley, Hoboken, 2009) developed a version of OSCV for smooth density functions. This article extends the method for nonsmooth densities. It also introduces the fully robust OSCV modification that produces consistent OSCV bandwidths for both smooth and nonsmooth cases. Practical implementations of the OSCV method for smooth and nonsmooth densities are discussed. One of the considered cross-validation kernels has potential for improving the OSCV method’s performance in the regression context.

Suggested Citation

  • Olga Y. Savchuk, 2020. "One-sided cross-validation for nonsmooth density functions," Computational Statistics, Springer, vol. 35(3), pages 1253-1272, September.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:3:d:10.1007_s00180-019-00938-3
    DOI: 10.1007/s00180-019-00938-3
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    References listed on IDEAS

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    1. C. Tenreiro, 2017. "A weighted least-squares cross-validation bandwidth selector for kernel density estimation," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(7), pages 3438-3458, April.
    2. Max Köhler & Anja Schindler & Stefan Sperlich, 2014. "A Review and Comparison of Bandwidth Selection Methods for Kernel Regression," International Statistical Review, International Statistical Institute, vol. 82(2), pages 243-274, August.
    3. Mammen, Enno & Martínez Miranda, María Dolores & Nielsen, Jens Perch & Sperlich, Stefan, 2011. "Do-Validation for Kernel Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 651-660.
    4. Olga Y. Savchuk & Jeffrey D. Hart, 2017. "Fully robust one-sided cross-validation for regression functions," Computational Statistics, Springer, vol. 32(3), pages 1003-1025, September.
    5. Savchuk, Olga Y. & Hart, Jeffrey D. & Sheather, Simon J., 2010. "Indirect Cross-Validation for Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 415-423.
    6. María Luz Gámiz & Enno Mammen & María Dolores Martínez Miranda & Jens Perch Nielsen, 2016. "Double one-sided cross-validation of local linear hazards," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 755-779, September.
    7. Olga Y. Savchuk & Jeffrey D. Hart & Simon P. Sheather, 2013. "One-sided cross-validation for nonsmooth regression functions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(4), pages 889-904, December.
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