High-Dimensional Log Contrast Models with Measurement Errors

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 guarantees for Eric Lasso, including estimation error bounds and asymptotic sign-consistent variable selection properties. The finite-sample performance of the method is demonstrated through simulation studies and a real-world application.

Key words and phrases: Compositional data, Error-in-variable, High-dimensional regression, Log contrast models, Lasso