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A Finite-sample bias correction method for general linear model in the presence of differential measurement errors

Author

Listed:
  • Ali Al-Sharadqah

    (California State University Northridge
    Prince Mohammad Bin Fahd University)

  • Karine Bagdasaryan

    (California State University Northridge)

  • Ola Nusierat

    (Prince Mohammad Bin Fahd University)

Abstract

This paper focuses on the general linear measurement error model, in which some or all predictors are measured with error, while others are measured precisely. We propose a semi-parametric estimator that works under general mechanisms of measurement error, including differential and non-differential errors. Other popular methods, such as the corrected score and conditional score methods, only work for non-differential measurement error models, but our estimator works in all scenarios. We develop our estimator by considering a family of objective functions that depend on an unspecified weight function. Using statistical error analysis and perturbation theory, we derive the optimal weight function under the small-sigma regime. The resulting estimator is statistically optimal in all senses. Even though we develop it under the small-sigma regime, we also establish its consistency and asymptotic normality under the large sample regime. Finally, we conduct a series of numerical experiments to confirm that the proposed estimator outperforms other existing methods.

Suggested Citation

  • Ali Al-Sharadqah & Karine Bagdasaryan & Ola Nusierat, 2025. "A Finite-sample bias correction method for general linear model in the presence of differential measurement errors," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 109(1), pages 149-195, March.
    • Handle: RePEc:spr:alstar:v:109:y:2025:i:1:d:10.1007_s10182-024-00510-5
    DOI: 10.1007/s10182-024-00510-5
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    References listed on IDEAS

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    1. Arturo Zavala & Heleno Bolfarine & Mário Castro, 2007. "Consistent estimation and testing in heteroscedastic polynomial errors-in-variables models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(3), pages 515-530, September.
    2. Chernov, N. & Lesort, C., 2004. "Statistical efficiency of curve fitting algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 47(4), pages 713-728, November.
    3. Yih-Huei Huang & Chi-Chung Wen & Yu-Hua Hsu, 2015. "The Extensively Corrected Score for Measurement Error Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 911-924, December.
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