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Weak convergence of the supremum distance for supersmooth kernel deconvolution

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  • van Es, Bert
  • Gugushvili, Shota

Abstract

We derive the asymptotic distribution of the supremum distance of the deconvolution kernel density estimator to its expectation for certain supersmooth deconvolution problems. It turns out that the asymptotics are essentially different from corresponding results for ordinary smooth deconvolution.

Suggested Citation

  • van Es, Bert & Gugushvili, Shota, 2008. "Weak convergence of the supremum distance for supersmooth kernel deconvolution," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2932-2938, December.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:17:p:2932-2938
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    References listed on IDEAS

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    1. Bert Van Es & Hae‐Won Uh, 2005. "Asymptotic Normality of Kernel‐Type Deconvolution Estimators," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 467-483, September.
    2. Hajo Holzmann & Leif Boysen, 2006. "Integrated Square Error Asymptotics for Supersmooth Deconvolution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 849-860, December.
    3. Nicolai Bissantz & Lutz Dümbgen & Hajo Holzmann & Axel Munk, 2007. "Non‐parametric confidence bands in deconvolution density estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 483-506, June.
    4. van Es, A. J. & Kok, A. R., 1998. "Simple kernel estimators for certain nonparametric deconvolution problems," Statistics & Probability Letters, Elsevier, vol. 39(2), pages 151-160, August.
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    Cited by:

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    3. Ali Al-Sharadqah & Majid Mojirsheibani & William Pouliot, 2020. "On the performance of weighted bootstrapped kernel deconvolution density estimators," Statistical Papers, Springer, vol. 61(4), pages 1773-1798, August.
    4. Dong, Hao & Otsu, Taisuke & Taylor, Luke, 2021. "Average Derivative Estimation Under Measurement Error," Econometric Theory, Cambridge University Press, vol. 37(5), pages 1004-1033, October.
    5. Katharina Proksch & Nicolai Bissantz & Hajo Holzmann, 2022. "Simultaneous inference for Berkson errors-in-variables regression under fixed design," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 773-800, August.
    6. Kato, Kengo & Sasaki, Yuya, 2018. "Uniform confidence bands in deconvolution with unknown error distribution," Journal of Econometrics, Elsevier, vol. 207(1), pages 129-161.
    7. Kengo Kato & Yuya Sasaki & Takuya Ura, 2021. "Robust inference in deconvolution," Quantitative Economics, Econometric Society, vol. 12(1), pages 109-142, January.
    8. Kengo Kato & Yuya Sasaki & Takuya Ura, 2018. "Inference based on Kotlarski's Identity," Papers 1808.09375, arXiv.org, revised Sep 2019.

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