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Kernel regression for errors-in-variables problems in the circular domain

Author

Listed:
  • Marco Di Marzio

    (DSFPEQ, University of Chieti-Pescara)

  • Stefania Fensore

    (DSFPEQ, University of Chieti-Pescara)

  • Charles C. Taylor

    (University of Leeds)

Abstract

We study the problem of estimating a regression function when the predictor and/or the response are circular random variables in the presence of measurement errors. We propose estimators whose weight functions are deconvolution kernels defined according to the nature of the involved variables. We derive the asymptotic properties of the proposed estimators and consider possible generalizations and extensions. We provide some simulation results and a real data case study to illustrate and compare the proposed methods.

Suggested Citation

  • Marco Di Marzio & Stefania Fensore & Charles C. Taylor, 2023. "Kernel regression for errors-in-variables problems in the circular domain," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(4), pages 1217-1237, October.
    • Handle: RePEc:spr:stmapp:v:32:y:2023:i:4:d:10.1007_s10260-023-00687-0
    DOI: 10.1007/s10260-023-00687-0
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    References listed on IDEAS

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    1. Macro Di Marzio & Agnese Panzera & Charles C. Taylor, 2012. "Non-parametric smoothing and prediction for nonlinear circular time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(4), pages 620-630, July.
    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. 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.
    4. 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.
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