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On optimal kernel choice for deconvolution

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  • Delaigle, Aurore
  • Hall, Peter

Abstract

In this note we show that, from a conventional viewpoint, there are particularly close parallels between optimal-kernel-choice problems in non-parametric deconvolution, and their better-understood counterparts in density estimation and regression. However, other aspects of these problems are distinctly different, and this property leads us to conclude that "optimal" kernels do not give satisfactory performance when applied to deconvolution. This unexpected result stems from the fact that standard side conditions, which are used to ensure that the familiar kernel-choice problem has a unique solution, do not have statistically beneficial implications for deconvolution estimators. In consequence, certain "sub-optimal" kernels produce estimators that enjoy both greater efficiency and greater visual smoothness.

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  • Delaigle, Aurore & Hall, Peter, 2006. "On optimal kernel choice for deconvolution," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1594-1602, September.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:15:p:1594-1602
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    2. Adusumilli, Karun & Kurisu, Daisuke & Otsu, Taisuke & Whang, Yoon-Jae, 2020. "Inference on distribution functions under measurement error," Journal of Econometrics, Elsevier, vol. 215(1), pages 131-164.
    3. Guillermo Basulto-Elias & Alicia L. Carriquiry & Kris Brabanter & Daniel J. Nordman, 2021. "Bivariate Kernel Deconvolution with Panel Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 122-151, May.
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    5. Xiaodong Gong & Jiti Gao, 2015. "Nonparametric Kernel Estimation of the Impact of Tax Policy on the Demand for Private Health Insurance in Australia," Monash Econometrics and Business Statistics Working Papers 6/15, Monash University, Department of Econometrics and Business Statistics.
    6. Adusumilli, Karun & Kurisu, Daisies & Otsu, Taisuke & Whang, Yoon-Jae, 2020. "Inference on distribution functions under measurement error," LSE Research Online Documents on Economics 102692, London School of Economics and Political Science, LSE Library.
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    10. Shota Gugushvili & Bert van Es & Peter Spreij, 2011. "Deconvolution for an atomic distribution: rates of convergence," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 1003-1029.

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