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Exact asymptotic limit for kernel estimation of regression level sets

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  • Dau, Hai Dang
  • Laloë, Thomas
  • Servien, Rémi

Abstract

The asymptotic behavior of a plug-in kernel estimator of the regression level sets is studied. The exact asymptotic limit of the symmetric difference is derived for a given level and for an unknown level corresponding to a fixed probability.

Suggested Citation

  • Dau, Hai Dang & Laloë, Thomas & Servien, Rémi, 2020. "Exact asymptotic limit for kernel estimation of regression level sets," Statistics & Probability Letters, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:stapro:v:161:y:2020:i:c:s0167715220300249
    DOI: 10.1016/j.spl.2020.108721
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    References listed on IDEAS

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    1. Cadre, BenoI^t, 2006. "Kernel estimation of density level sets," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 999-1023, April.
    2. Polonik, Wolfgang & Wang, Zailong, 2005. "Estimation of regression contour clusters--an application of the excess mass approach to regression," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 227-249, June.
    3. Elena Di Bernardino & Thomas Laloë & Rémi Servien, 2015. "Erratum to: Estimating covariate functions associated to multivariate risks: a level set approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(5), pages 527-527, July.
    4. Elena Di Bernardino & Thomas Laloë & Véronique Maume-Deschamps & Clémentine Prieur, 2013. "Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory," Post-Print hal-00580624, HAL.
    5. Yen-Chi Chen & Christopher R. Genovese & Larry Wasserman, 2017. "Density Level Sets: Asymptotics, Inference, and Visualization," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1684-1696, October.
    6. Elena Bernardino & Thomas Laloë & Rémi Servien, 2015. "Estimating covariate functions associated to multivariate risks: a level set approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(5), pages 497-526, July.
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