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Flexible parametric approach to classical measurement error variance estimation without auxiliary data

Author

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  • Aurélie Bertrand
  • Ingrid Van Keilegom
  • Catherine Legrand

Abstract

Measurement error in the continuous covariates of a model generally yields bias in the estimators. It is a frequent problem in practice, and many correction procedures have been developed for different classes of models. However, in most cases, some information about the measurement error distribution is required. When neither validation nor auxiliary data (e.g., replicated measurements) are available, this specification turns out to be tricky. In this article, we develop a flexible likelihood‐based procedure to estimate the variance of classical additive error of Gaussian distribution, without additional information, when the covariate has compact support. The performance of this estimator is investigated both in an asymptotic way and through finite sample simulations. The usefulness of the obtained estimator when using the simulation extrapolation (SIMEX) algorithm, a widely used correction method, is then analyzed in the Cox proportional hazards model through other simulations. Finally, the whole procedure is illustrated on real data.

Suggested Citation

  • Aurélie Bertrand & Ingrid Van Keilegom & Catherine Legrand, 2019. "Flexible parametric approach to classical measurement error variance estimation without auxiliary data," Biometrics, The International Biometric Society, vol. 75(1), pages 297-307, March.
    • Handle: RePEc:bla:biomet:v:75:y:2019:i:1:p:297-307
    DOI: 10.1111/biom.12960
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    References listed on IDEAS

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    1. Schwarz, M. & Van Bellegem, S., 2010. "Consistent density deconvolution under partially known error distribution," LIDAM Reprints ISBA 2010013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Bertrand, Aurelie & Legrand, Catherine & Leonard, Daniel & Van Keilegom, Ingrid, 2017. "Robustness of estimation methods in a survival cure model with mismeasured covariates," LIDAM Reprints ISBA 2017021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    Cited by:

    1. Jeon, Jeong Min & Van Keilegom, Ingrid, 2023. "Density estimation for mixed Euclidean and non-Euclidean data in the presence of measurement error," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    2. Jeong Min Jeon & Ingrid Van Keilegom, 2024. "Density estimation and regression analysis on hyperspheres in the presence of measurement error," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(2), pages 513-556, June.

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