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Empirical Likelihood for Varying Coefficient EV Models under Longitudinal Data

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Abstract

In this paper, a varying coefficient errors-in-variables model under longitudinal data is investigated. An empirical likelihood based bias-correction approach is proposed. It is proved that the proposed statistics are asymptotically chi-squared under some mild conditions, and hence can be used to construct the confidence regions of the parameters of interest. Finite sample performance of the proposed method is illustrated in a simulation study. The proposed methods are applied to an AIDS clinical trial dataset.

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References

  1. Cui, H.J., Chen, X.S. Empirical likelihood confidence region for parameter in the errors-in-variables. Journal of Multivariate Analysis, 84: 101–115 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. Delaigle, A., Meister, A. Nonparametric regression estimation in the heteroscedastic errors-in-variables problem. Journal of the American Statistical Association, 102(480): 1416–1426 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Eubank, R.L., Huang, C., Maldonadok, Y.M., Wang, N., Wang, S. Buchanan, R.J. Smoothing Splines Estimation in Varying coefficient models. Journal of the Royal Statistical Society, Ser.B, 66: 653–667 (2004)

    Article  Google Scholar 

  4. Fan, J, Zhang, J.T. Two-step estimation of functional linear models with applications to longitudinal data. Journal of the Royal Statistical Society, Ser.B, 62: 303–322 (2000)

    Article  MathSciNet  Google Scholar 

  5. Hoover, D.R., Rice, J.A., Wu, C.O., Yang, L.P. Nonparametric smoothing estimation of time-varying coefficient model with longitudinal data. Biometrika, 85: 809–822 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Huang, J.Z., Wu, C.O., Zhou, L. Varying coefficient models and basis function approximations for the analysis of repeated measurements. Biometrika, 89: 111–128 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Huang, J.Z., Wu, C.O., Zhou, L. Polynomial spline estimation and inference for varying coefficient models with longitudinal data. Statistica Sinica, 14: 763–788 (2004)

    MathSciNet  MATH  Google Scholar 

  8. Liang, H., Hardle, W., Carroll, R.J. Estimation in a semiparametric partially linear errors-in-variables model. The Annals of Statistics, 27(5): 1519–1535 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  9. Liang, H., Wang, S.J., Carroll, R.J. Partially linear models with missing responses variables and error-prone covariates. Biometrika, 94(1): 184–222 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  10. Lin, X., Carroll, R.J. Nonparametric function estimation for clustered data when the predictor is measured without/with error. Journal of the American Statistical Association, 95: 520–534 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  11. Liu, Q. Asymptotic normality for the partially linear EV models with longitudinal data. Communications in Statistics-Theory and Methods, 40(7): 1149–1158 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Liu, Q. Estimation of the Linear EV model with censored data. Journal of Statistical Planning and Inference, 141(7): 2463–2471 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. Liu, Q., Jiang, Y.Y., Wu, K.F. The wavelet estimations of a kind of semiparametric errors-in-variables functional relationship model. Acta Math. Appl. Sinica, 28(2): 296–307 (2005) (in Chinese)

    MathSciNet  Google Scholar 

  14. Liu, Q., Xue, L.G., Chen, F. Empirical likelihood confidence regions of parameters in a censored partially linear EV model. Acta Math. Sinica, 52(3): 549–560 (2009) (in Chinese)

    MathSciNet  MATH  Google Scholar 

  15. Lv, Y., Zhang R., Huang Z. Nonparametric estimation of varying coefficient error-in-variable models with validation sampling. Journal of Statistical Planning and Inference, 141(10): 3323–3344 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. Owen, A.B. Empirical likelihood ratio confidence intervals for a single function. Biometrika, 75(2): 237–249 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  17. Owen, A.B. Empirical likelihood ratio confidence regions. The Annals of Statistics, 18(1): 90–120 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  18. Rice, J.A., Silveman, B.W. Estimating the mean and covariance structure nonparasitically when the data are curves. Journal of the Royal Statistical Society, Ser.B, 53: 233–243 (1991)

    Google Scholar 

  19. Stute, W., Xue, L.G., Zhu, L.X. Empirical likelihood inference in nonlinear errors-in-Covariables models with validation data. Journal of the American Statistical Association, 102(477): 332–346 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  20. Wang, Q.H. Estimation of linear error-in-covariables models with validation data under random censorship. Journal of Multivariate Analysis, 74: 245–266 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  21. Wang, Q.H., Rao, J.N.K. Empirical likelihood-Based inference in linear errors-in-covariables models with Validation data. Biometrika, 89(2): 345–358(2002)

    Article  MathSciNet  MATH  Google Scholar 

  22. Wang, Q.H., Yu, K.M. Likelihood-based kernel estimation in semiparametric errors-in-covariables models with validation data. Journal of Multivariate Analysis, 98: 455–480 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  23. Wang, Q.H., Rao, J.N.K. Empirical likelihood based-inference in linear models with missing data. Scandinavian Journal of Statistics, 29: 563–576 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  24. Wei, C.H. Estimation in varying-coefficient errors-in-variables models with missing response variables. Communication in Statistics-Simulation and computation, 40: 383–393 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  25. Wu, C.O., Chiang, C.T., Hoover, D.R. Asymptotic confidence regions for kernel smoothing of a varyingcoefficient model with longitudinal data. Journal of the American Statistical Association, 93(444): 1388–1402 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  26. Wu, C.O., Chiang, C.T. Kernel smoothing on varying-coefficient models with longitudinal Dependent variables. Statistica Sinica, 10: 433–456 (2000)

    MathSciNet  MATH  Google Scholar 

  27. Wang X., Li G., Lin L. Empirical likelihood inference for semi-parametric varying-coefficient partially linear EV models. Metrika, 73: 171–185 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  28. Xue, L.G., Zhu, L.X. Empirical likelihood for a varying coefficient model with longitudinal data. Journal of the American Statistical Association, 102(478): 642–654 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  29. Xue, L.G. Empirical likelihood confidence Intervals for response mean with data missing at random. Scandinavian Journal of Statistics, 36: 671–685 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  30. Zhu, L.X., Xue, L.G. Empirical likelihood confidence regions in a partially linear single-index model. Journal of the Royal Statistical Society, Ser.B, 68: 549–570 (2006)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Statistics, Capital University of Economics and Business, Beijing, 100070, China

    Qiang Liu

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  1. Qiang Liu
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Correspondence to Qiang Liu.

Additional information

Supported by National Social Science Foundation of China (16BTJ015).

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Liu, Q. Empirical Likelihood for Varying Coefficient EV Models under Longitudinal Data. Acta Math. Appl. Sin. Engl. Ser. 34, 585–596 (2018). https://doi.org/10.1007/s10255-018-0770-x

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  • DOI: https://doi.org/10.1007/s10255-018-0770-x

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