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Statistical estimation in varying coefficient models with surrogate data and validation sampling

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  • Wang, Qihua
  • Zhang, Riquan

Abstract

Varying coefficient error-in-covariables models are considered with surrogate data and validation sampling. Without specifying any error structure equation, two estimators for the coefficient function vector are suggested by using the local linear kernel smoothing technique. The proposed estimators are proved to be asymptotically normal. A bootstrap procedure is suggested to estimate the asymptotic variances. The data-driven bandwidth selection method is discussed. A simulation study is conducted to evaluate the proposed estimating methods.

Suggested Citation

  • Wang, Qihua & Zhang, Riquan, 2009. "Statistical estimation in varying coefficient models with surrogate data and validation sampling," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2389-2405, November.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:10:p:2389-2405
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    References listed on IDEAS

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    1. Wang, Qihua & Yu, Keming, 2007. "Likelihood-based kernel estimation in semiparametric errors-in-covariables models with validation data," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 455-480, March.
    2. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
    3. Chiang C-T. & Rice J. A & Wu C. O, 2001. "Smoothing Spline Estimation for Varying Coefficient Models With Repeatedly Measured Dependent Variables," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 605-619, June.
    4. Jianhua Z. Huang, 2002. "Varying-coefficient models and basis function approximations for the analysis of repeated measurements," Biometrika, Biometrika Trust, vol. 89(1), pages 111-128, March.
    5. Qihua Wang, 2002. "Empirical likelihood-based inference in linear errors-in-covariables models with validation data," Biometrika, Biometrika Trust, vol. 89(2), pages 345-358, June.
    6. Wang, Qihua, 2006. "Nonparametric regression function estimation with surrogate data and validation sampling," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1142-1161, May.
    7. Wang, Qihua, 2000. "Estimation of Linear Error-in-Covariables Models with Validation Data Under Random Censorship," Journal of Multivariate Analysis, Elsevier, vol. 74(2), pages 245-266, August.
    8. Yi‐Hau Chen, 2002. "Cox regression in cohort studies with validation sampling," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 51-62, January.
    9. Wang, Qihua, 1999. "Estimation of Partial Linear Error-in-Variables Models with Validation Data," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 30-64, April.
    10. J. Fan & J.‐T. Zhang, 2000. "Two‐step estimation of functional linear models with applications to longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 303-322.
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    Cited by:

    1. Peixin Zhao & Liugen Xue, 2013. "Instrumental variable-based empirical likelihood inferences for varying-coefficient models with error-prone covariates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(2), pages 380-396, February.
    2. Zhang, Weiwei & Li, Gaorong & Xue, Liugen, 2011. "Profile inference on partially linear varying-coefficient errors-in-variables models under restricted condition," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 3027-3040, November.
    3. Zhao, Yan-Yong & Lin, Jin-Guan & Huang, Xing-Fang & Wang, Hong-Xia, 2016. "Adaptive jump-preserving estimates in varying-coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 65-80.
    4. Yang, Yiping & Li, Gaorong & Peng, Heng, 2014. "Empirical likelihood of varying coefficient errors-in-variables models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 1-18.

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