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Likelihood-based kernel estimation in semiparametric errors-in-covariables models with validation data

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  • Wang, Qihua
  • Yu, Keming

Abstract

We present methods to handle error-in-variables models. Kernel-based likelihood score estimating equation methods are developed for estimating conditional density parameters. In particular, a semiparametric likelihood method is proposed for sufficiently using the information in the data. The asymptotic distribution theory is derived. Small sample simulations and a real data set are used to illustrate the proposed estimation methods.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:98:y:2007:i:3:p:455-480
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    References listed on IDEAS

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    1. Qihua Wang & J. N. K. Rao, 2002. "Empirical Likelihood‐based Inference in Linear Models with Missing Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 563-576, September.
    2. C.‐Y. Wang & Margaret Sullivan Pepe, 2000. "Expected estimating equations to accommodate covariate measurement error," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(3), pages 509-524.
    3. Zhang, Biao, 1997. "Empirical likelihood confidence intervals for M-functionals in the presence of auxiliary information," Statistics & Probability Letters, Elsevier, vol. 32(1), pages 87-97, February.
    4. Wang, Qihua & Härdle, Wolfgang, 2002. "Empirical likelihood-based dimension reduction inference for linear error-in-responses models with validation study," SFB 373 Discussion Papers 2002,82, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    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, 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.
    7. 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.
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    Cited by:

    1. Sun, Zhihua & Wang, Qihua & Dai, Pengjie, 2009. "Model checking for partially linear models with missing responses at random," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 636-651, April.
    2. 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.
    3. Wai-Yin Poon & Hai-Bin Wang, 2010. "Bayesian Analysis of Multivariate Probit Models with Surrogate Outcome Data," Psychometrika, Springer;The Psychometric Society, vol. 75(3), pages 498-520, September.
    4. 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.

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