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Abstract
The extraordinary amounts of data generated nowadays pose heavy demands on computational resources and time, which hinders the implementation of various statistical methods. An efficient and popular strategy of downsizing data volumes and thus alleviating these challenges is subsampling. However, the existing methods either rely on specific assumptions for the underlying models or acquire partial information from the available data. For regression problems, we propose a novel approach, termed adaptive subsampling with the minimum energy criterion (ASMEC). The proposed method requires no explicit model assumptions and “smartly” incorporates information on covariates and responses. ASMEC subsamples possess two desirable properties: space-fillingness and spatial adaptiveness. We investigate the limiting distribution of ASMEC subsamples and their theoretical properties under the smoothing spline regression model. The effectiveness and robustness of the ASMEC approach are also supported by a variety of synthetic examples and two real-life examples.
Supplementary Materials
Supplementary Material.pdf: The file supplements more details of the smoothing spline regression model, proofs of Theorems 1–3, algorithm of ASMEC subsampling for higher-dimensional data, and an illustration of functions used in the simulations of the main manuscript.
ASMEC code.zip: The file includes code to perform the proposed methods and all datasets used as examples in the article.
Acknowledgments
The authors sincerely thank the editor, an associated editor and two anonymous referees for their valuable comments and suggestions.
Disclosure Statement
The authors report there are no competing interests to declare.