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<p>In the presence of covariates affected by measurement errors, we first propose the corrected least product relative error score (CLAPRES) function to mitigate the effects of measurement errors on parameter estimation in multiplicative regression models. This method is invariant under scale transformations of the positive response and the covariates. To address the challenge of massive datasets with measurement errors, we explore an optimal subsampling algorithm based on the CLAPRES method and derive the optimal subsampling probabilities under the A- and L-optimality criteria. The consistency and asymptotic normality of the subsampling CLAPRES estimators are established. Numerical studies demonstrate the effectiveness of the CLAPRES method.</p>

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Optimal subsampling for multiplicative linear measurement error models

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月20日

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  • Mingqiu Wang,
  • Xiuli Wang,
  • Yang Han

摘要

In the presence of covariates affected by measurement errors, we first propose the corrected least product relative error score (CLAPRES) function to mitigate the effects of measurement errors on parameter estimation in multiplicative regression models. This method is invariant under scale transformations of the positive response and the covariates. To address the challenge of massive datasets with measurement errors, we explore an optimal subsampling algorithm based on the CLAPRES method and derive the optimal subsampling probabilities under the A- and L-optimality criteria. The consistency and asymptotic normality of the subsampling CLAPRES estimators are established. Numerical studies demonstrate the effectiveness of the CLAPRES method.