  Subsampling algorithms for various parametric regression models with massive
data have been extensively investigated in recent years. However, all existing
studies on subsampling heavily rely on clean massive data. In practical
applications, the observed covariates may suffer from inaccuracies due to
measurement errors. To address the challenge of large datasets with measurement
errors, this study explores two subsampling algorithms based on the corrected
likelihood approach: the optimal subsampling algorithm utilizing inverse
probability weighting and the perturbation subsampling algorithm employing
random weighting assuming a perfectly known distribution. Theoretical
properties for both algorithms are provided. Numerical simulations and two
real-world examples demonstrate the effectiveness of these proposed methods
compared to other uncorrected algorithms.
