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Estimation of nonparametric regression models with a mixture of Berkson and classical errors

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  • Yin, Zanhua
  • Gao, Wei
  • Tang, Man-Lai
  • Tian, Guo-Liang

Abstract

We consider the estimation of nonparametric regression models with the explanatory variable being measured with Berkson errors or with a mixture of Berkson and classical errors. By constructing a compact operator, the regression function is the solution of an ill-posed inverse problem, and we propose an estimation procedure based on Tikhonov regularization. Under mild conditions, the convergence rate of proposed estimator is derived. The finite-sample properties of the estimator are investigated through simulation studies.

Suggested Citation

  • Yin, Zanhua & Gao, Wei & Tang, Man-Lai & Tian, Guo-Liang, 2013. "Estimation of nonparametric regression models with a mixture of Berkson and classical errors," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1151-1162.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:4:p:1151-1162
    DOI: 10.1016/j.spl.2013.01.013
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    References listed on IDEAS

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    1. Delaigle, Aurore & Meister, Alexander, 2007. "Nonparametric Regression Estimation in the Heteroscedastic Errors-in-Variables Problem," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1416-1426, December.
    2. Raymond J. Carroll & Aurore Delaigle & Peter Hall, 2007. "Non‐parametric regression estimation from data contaminated by a mixture of Berkson and classical errors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 859-878, November.
    3. Delaigle, Aurore & Fan, Jianqing & Carroll, Raymond J., 2009. "A Design-Adaptive Local Polynomial Estimator for the Errors-in-Variables Problem," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 348-359.
    4. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77, Elsevier.
    5. Carrasco, Marine & Florens, Jean-Pierre, 2011. "A Spectral Method For Deconvolving A Density," Econometric Theory, Cambridge University Press, vol. 27(3), pages 546-581, June.
    6. Bani Mallick & F. Owen Hoffman & Raymond J. Carroll, 2002. "Semiparametric Regression Modeling with Mixtures of Berkson and Classical Error, with Application to Fallout from the Nevada Test Site," Biometrics, The International Biometric Society, vol. 58(1), pages 13-20, March.
    7. Aurore Delaigle & Peter Hall & Peihua Qiu, 2006. "Nonparametric methods for solving the Berkson errors‐in‐variables problem," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 201-220, April.
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