Corrected optimal subsampling for a class of generalized linear measurement error models

Ruiyuan Chang; Xiuli Wang; Mingqiu Wang; Ruiyuan Chang; Xiuli Wang; Mingqiu Wang

doi:10.3934/math.2025203

AIMS Mathematics

2025, Volume 10, Issue 2: 4412-4440. doi: 10.3934/math.2025203

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Research article

Corrected optimal subsampling for a class of generalized linear measurement error models

School of Statistics and Data Science, Qufu Normal University, Qufu 273100, China

Received: 29 December 2024 Revised: 15 February 2025 Accepted: 24 February 2025 Published: 28 February 2025
MSC : 62F12, 62J12

Subsampling techniques have been promoted in massive data and can substantially reduce the computing time. However, existing subsampling techniques do not consider the case of dirty data, especially the inaccuracy of covariates due to measurement errors, which will lead to the inconsistent estimators of regression coefficients. Therefore, to eliminate the influence of measurement errors on parameter estimators for massive data, this paper combined the corrected score function with the subsampling technique. The consistency and asymptotic normality of the estimators in the general subsampling are also derived. In addition, optimal subsampling probabilities are obtained based on the general subsampling algorithm using the A-optimality and L-optimality criteria and the truncation method, and then an adaptive two-step algorithm is developed. The effectiveness of the proposed method is demonstrated through numerical simulations and two real data analyses.
- A-optimality criteria,
- generalized linear models,
- L-optimality criteria,
- massive data,
- measurement errors,
- optimal subsampling
Citation: Ruiyuan Chang, Xiuli Wang, Mingqiu Wang. Corrected optimal subsampling for a class of generalized linear measurement error models[J]. AIMS Mathematics, 2025, 10(2): 4412-4440. doi: 10.3934/math.2025203

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Abstract

Subsampling techniques have been promoted in massive data and can substantially reduce the computing time. However, existing subsampling techniques do not consider the case of dirty data, especially the inaccuracy of covariates due to measurement errors, which will lead to the inconsistent estimators of regression coefficients. Therefore, to eliminate the influence of measurement errors on parameter estimators for massive data, this paper combined the corrected score function with the subsampling technique. The consistency and asymptotic normality of the estimators in the general subsampling are also derived. In addition, optimal subsampling probabilities are obtained based on the general subsampling algorithm using the A-optimality and L-optimality criteria and the truncation method, and then an adaptive two-step algorithm is developed. The effectiveness of the proposed method is demonstrated through numerical simulations and two real data analyses.

References

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