High-dimensional log contrast models with measurement errors

TL;DR

This paper introduces the Error-in-composition (Eric) Lasso, a novel method for high-dimensional regression with compositional data affected by measurement errors, providing theoretical guarantees and practical performance insights.

Contribution

The paper develops the first method to handle measurement errors in high-dimensional compositional regression, with theoretical error bounds and sign consistency.

Findings

Eric Lasso achieves accurate estimation in simulations.

The method demonstrates effective variable selection.

Application to real data shows practical utility.

Abstract

High-dimensional compositional data are frequently encountered in many fields of modern scientific research. In regression analysis of compositional data, the presence of covariate measurement errors poses grand challenges for existing statistical error-in-variable regression analysis methods since measurement error in one component of the composition has an impact on others. To simultaneously address the compositional nature and measurement errors in the high-dimensional design matrix of compositional covariates, we propose a new method named Error-in-composition (Eric) Lasso for regression analysis of corrupted compositional predictors. Estimation error bounds of Eric Lasso and its asymptotic sign-consistent selection properties are established. We then illustrate the finite sample performance of Eric Lasso using simulation studies and demonstrate its potential usefulness in a real data application example.