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Shape-restricted nonparametric regression with overall noisy measurements

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  • Georg Ch. Pflug
  • Roger J.-B. Wets

Abstract

For a nonparametric regression problem with errors in variables, we consider a shape-restricted regression function estimate, which does not require the choice of bandwidth parameters. We demonstrate that this estimate is consistent for classes of regression function candidates, which are closed under the graph topology.

Suggested Citation

  • Georg Ch. Pflug & Roger J.-B. Wets, 2013. "Shape-restricted nonparametric regression with overall noisy measurements," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(2), pages 323-338, June.
    • Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:323-338
    DOI: 10.1080/10485252.2012.754890
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    References listed on IDEAS

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    1. Wang, J. & Ghosh, S.K., 2012. "Shape restricted nonparametric regression with Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2729-2741.
    2. Beresteanu, Arie, 2004. "Nonparametric Estimation of Regression Functions under Restrictions on Partieal Derivatives," Working Papers 04-06, Duke University, Department of Economics.
    3. Engel, J & Kneip, A, 1995. "Model Estimation in Nonlinear Regression," Papers 9510, Catholique de Louvain - Institut de statistique.
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