Optimal subsampling for multiplicative linear measurement error models

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, this study explores an optimal subsampling algorithm based on the CLAPRES method and derives 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.