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Simultaneous treatment of unspecified heteroskedastic model error distribution and mismeasured covariates for restricted moment models

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  • Garcia, Tanya P.
  • Ma, Yanyuan

Abstract

We develop consistent and efficient estimation of parameters in general regression models with mismeasured covariates. We assume the model error and covariate distributions are unspecified, and the measurement error distribution is a general parametric distribution with unknown variance–covariance. We construct root-n consistent, asymptotically normal and locally efficient estimators using the semiparametric efficient score. We do not estimate any unknown distribution or model error heteroskedasticity. Instead, we form the estimator under possibly incorrect working distribution models for the model error, error-prone covariate, or both. Empirical results demonstrate robustness to different incorrect working models in homoscedastic and heteroskedastic models with error-prone covariates.

Suggested Citation

  • Garcia, Tanya P. & Ma, Yanyuan, 2017. "Simultaneous treatment of unspecified heteroskedastic model error distribution and mismeasured covariates for restricted moment models," Journal of Econometrics, Elsevier, vol. 200(2), pages 194-206.
    • Handle: RePEc:eee:econom:v:200:y:2017:i:2:p:194-206
    DOI: 10.1016/j.jeconom.2017.06.005
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    References listed on IDEAS

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    1. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
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    3. S. M. Schennach & Yingyao Hu, 2013. "Nonparametric Identification and Semiparametric Estimation of Classical Measurement Error Models Without Side Information," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 177-186, March.
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    5. Yuedong Wang & Yanyuan Ma & Raymond J. Carroll, 2009. "Variance estimation in the analysis of microarray data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 425-445, April.
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    Cited by:

    1. Layla Parast & Tanya P. Garcia & Ross L. Prentice & Raymond J. Carroll, 2022. "Robust methods to correct for measurement error when evaluating a surrogate marker," Biometrics, The International Biometric Society, vol. 78(1), pages 9-23, March.

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    More about this item

    Keywords

    Influence function; Linear operator; Measurement error; Nuisance tangent space; Restricted moment model;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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