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

Ali Al-Sharadqah (), Karine Bagdasaryan () and Ola Nusierat ()
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Ali Al-Sharadqah: California State University Northridge
Karine Bagdasaryan: California State University Northridge
Ola Nusierat: Prince Mohammad Bin Fahd University

AStA Advances in Statistical Analysis, 2025, vol. 109, issue 1, No 6, 149-195

Abstract: 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.

Keywords: Differential measurement errors; Finite-sample bias correction; Measurement error models; Semi-parametric method; Small-sigma regime; 62J05; 62E17; 62E20 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10182-024-00510-5

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