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Local polynomial regression and simulation–extrapolation

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  • John Staudenmayer
  • David Ruppert

Abstract

Summary. The paper introduces a new local polynomial estimator and develops supporting asymptotic theory for nonparametric regression in the presence of covariate measurement error. We address the measurement error with Cook and Stefanski's simulation–extrapolation (SIMEX) algorithm. Our method improves on previous local polynomial estimators for this problem by using a bandwidth selection procedure that addresses SIMEX's particular estimation method and considers higher degree local polynomial estimators. We illustrate the accuracy of our asymptotic expressions with a Monte Carlo study, compare our method with other estimators with a second set of Monte Carlo simulations and apply our method to a data set from nutritional epidemiology. SIMEX was originally developed for parametric models. Although SIMEX is, in principle, applicable to nonparametric models, a serious problem arises with SIMEX in nonparametric situations. The problem is that smoothing parameter selectors that are developed for data without measurement error are no longer appropriate and can result in considerable undersmoothing. We believe that this is the first paper to address this difficulty.

Suggested Citation

  • John Staudenmayer & David Ruppert, 2004. "Local polynomial regression and simulation–extrapolation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 17-30, February.
    • Handle: RePEc:bla:jorssb:v:66:y:2004:i:1:p:17-30
    DOI: 10.1046/j.1369-7412.2003.05282.x
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    Cited by:

    1. Julie McIntyre & Brent A. Johnson & Stephen M. Rappaport, 2018. "Monte Carlo methods for nonparametric regression with heteroscedastic measurement error," Biometrics, The International Biometric Society, vol. 74(2), pages 498-505, June.
    2. Carroll, Raymond J. & Delaigle, Aurore & Hall, Peter, 2009. "Nonparametric Prediction in Measurement Error Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 993-1003.
    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. Raymond J. Carroll & Peter Hall, 2004. "Low order approximations in deconvolution and regression with errors in variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 31-46, February.
    5. Yicheng Kang & Xiaodong Gong & Jiti Gao & Peihua Qiu, 2016. "Error-in-Variables Jump Regression Using Local Clustering," Monash Econometrics and Business Statistics Working Papers 13/16, Monash University, Department of Econometrics and Business Statistics.
    6. Wang, Xiao-Feng & Fan, Zhaozhi & Wang, Bin, 2010. "Estimating smooth distribution function in the presence of heteroscedastic measurement errors," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 25-36, January.
    7. Lechner Sandra & Pohlmeier Winfried, 2005. "Data Masking by Noise Addition and the Estimation of Nonparametric Regression Models," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 225(5), pages 517-528, October.
    8. Yiping Yang & Tiejun Tong & Gaorong Li, 2019. "SIMEX estimation for single-index model with covariate measurement error," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(1), pages 137-161, March.

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