Abstract

High-dimensional compositional data are increasingly prevalent across

diverse fields of modern scientific research. Regression analysis involving compositional data presents unique challenges, particularly when covariate measurement

errors are present. These errors can propagate across composition components

due to their inherent dependency structure, complicating the application of conventional error-in-variables regression techniques. To simultaneously address the

compositional nature and measurement errors in the high-dimensional design

matrix of compositional covariates, we propose the Error-in-Composition (Eric)

Lasso, a novel method for regression analysis with high-dimensional compositional covariates subject to measurement error. We establish theoretical guar-

antees for Eric Lasso, including estimation error bounds and asymptotic signconsistent variable selection properties.

The finite-sample performance of the

method is demonstrated through simulation studies and a real-world application.

The authors are listed in alphabetical order. Correspondence should be addressed

Information

Preprint No.SS-2025-0223
Manuscript IDSS-2025-0223
Complete AuthorsWenxi Tan, Lingzhou Xue, Songshan Yang, Xiang Zhan
Corresponding AuthorsLingzhou Xue
Emailslzxue@psu.edu

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Acknowledgments

The authors would like to thank the Co-Editor, the Associate Editor, and

the anonymous referees for their helpful suggestions and constructive comments. The research of Tan and Xue was supported by the U.S. National

Science Foundation (NSF) grant DMS-2210775 and the U.S. National Institutes of Health (NIH) grant 1R01GM152812. The research of Yang was

supported by the National Key R&D Program of China 2023YFA1008702

and the National Natural Foundation of China (NSFC) 12301389. The research of Zhan was supported by the National Natural Science Foundation

of China (grant no. 12371287).

Supplementary Materials

The online supplementary materials consist of technical proofs of theorems

and additional numerical results.

Supplementary materials are available for download.