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 measure-

ment 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 appli-

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

cation.

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