The A-optimal subsampling approach to the analysis of count data of massive size

Abstract

The uniform and the statistical leverage-scores-based (nonuniform) distributions are often used in the development of randomised algorithms and the analysis of data of massive size. Both distributions, however, are not effective in extraction of important information in data. In this article, we construct the A-optimal subsampling estimators of parameters in generalised linear models (GLM) to approximate the full-data estimators, and derive the A-optimal distributions based on the criterion of minimising the sum of the component variances of the subsampling estimators. As calculating the distributions has the same time complexity as the full-data estimator, we generalise the Scoring Algorithm introduced in Zhang, Tan, and Peng ((2023), ‘Sample Size Determination forMultidimensional Parameters and A-Optimal Subsampling in a Big Data Linear Regression Model’, To appear in the Journal of Statistical Computation and Simulation. Preprint. Available at https://math.indianapolis.iu.edu/hanxpeng/SSD_23_4.pdf) in a Big Data linear model to GLM using the iterative weighted least squares. The paper presents a comprehensive numerical evaluation of our approach using simulated and real data through the comparison of its performance with the uniform and the leverage-scores- subsamplings. The results exhibited that our approach substantially outperformed the uniform and the leverage-scores subsamplings and the Algorithm significantly reduced the computing time required for implementing the full-data estimator.