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SIMEX estimation for single-index model with covariate measurement error

Author

Listed:
  • Yiping Yang

    (Chongqing Technology and Business University)

  • Tiejun Tong

    (Hong Kong Baptist University)

  • Gaorong Li

    (Beijing University of Technology)

Abstract

In this paper, we consider the single-index measurement error model with mismeasured covariates in the nonparametric part. To solve the problem, we develop a simulation-extrapolation (SIMEX) algorithm based on the local linear smoother and the estimating equation. For the proposed SIMEX estimation, it is not needed to assume the distribution of the unobserved covariate. We transform the boundary of a unit ball in $${\mathbb {R}}^p$$ R p to the interior of a unit ball in $${\mathbb {R}}^{p-1}$$ R p - 1 by using the constraint $$\Vert \beta \Vert =1$$ ‖ β ‖ = 1 . The proposed SIMEX estimator of the index parameter is shown to be asymptotically normal under some regularity conditions. We also derive the asymptotic bias and variance of the estimator of the unknown link function. Finally, the performance of the proposed method is examined by simulation studies and is illustrated by a real data example.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:alstar:v:103:y:2019:i:1:d:10.1007_s10182-018-0327-6
    DOI: 10.1007/s10182-018-0327-6
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    References listed on IDEAS

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    Cited by:

    1. Chen, Li-Pang, 2019. "Semiparametric estimation for cure survival model with left-truncated and right-censored data and covariate measurement error," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    2. Ke Wang & Dehui Wang, 2024. "Estimation for partially linear single-index spatial autoregressive model with covariate measurement errors," Statistical Papers, Springer, vol. 65(7), pages 4201-4241, September.
    3. Shi, Jianhong & Zhang, Yujing & Yu, Ping & Song, Weixing, 2021. "SIMEX estimation in parametric modal regression with measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    4. Jun Zhang, 2021. "Model checking for multiplicative linear regression models with mixed estimators," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(3), pages 364-403, August.
    5. Jun Zhang, 2021. "Estimation and variable selection for partial linear single-index distortion measurement errors models," Statistical Papers, Springer, vol. 62(2), pages 887-913, April.

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