Optimal distributed subsampling for high-dimensional linear measurement error models via doubly bias-corrected score

For high-dimensional linear measurement error models with massive data, we develop a doubly bias-corrected score function based on a distributed subsample for the preconceived low-dimensional parameter in the presence of high-dimensional nuisance parameter. The resulting distributed subsample estimator is consistent and asymptotically normal with an explicitly derived asymptotic covariance matrix. To pursue more efficient distributed subsampling, we propose a unified optimal distributed subsampling scheme, which includes the A- and L-optimality criteria and can be implemented using an initial distributed subsample for constructing the doubly bias-corrected score function. The resulting estimator under optimal distributed subsampling is asymptotically normal with some optimality property. The finite-sample performance of the proposed method is studied by simulation and National Longitudinal Survey of Youth Dataset.