Robust Nonparametric Regression for Compositional Data: the Simplicial--Real case

TL;DR

This paper develops a robust nonparametric regression method tailored for compositional data, addressing the challenges posed by their simplex structure and susceptibility to outliers, with demonstrated effectiveness through simulations and real data.

Contribution

It introduces a novel robust estimator for nonparametric regression with compositional covariates, accounting for the simplex geometry and outlier resistance.

Findings

Robust estimator outperforms classical methods under contamination.

Numerical simulations confirm improved accuracy with outliers.

Real data analysis shows practical advantages of the proposed approach.

Abstract

Statistical analysis on compositional data has gained a lot of attention due to their great potential of applications. A feature of these data is that they are multivariate vectors that lie in the simplex, that is, the components of each vector are positive and sum up a constant value. This fact poses a challenge to the analyst due to the internal dependency of the components which exhibit a spurious negative correlation. Since classical multivariate techniques are not appropriate in this scenario, it is necessary to endow the simplex of a suitable algebraic-geometrical structure, which is a starting point to develop adequate methodology and strategies to handle compositions. We centered our attention on regression problems with real responses and compositional covariates and we adopt a nonparametric approach due to the flexibility it provides. Aware of the potential damage that outliers may produce, we introduce a robust estimator in the framework of nonparametric regression for compositional data. The performance of the estimators is investigated by means of a numerical study where different contamination schemes are simulated. Through a real data analysis the advantages of using a robust procedure is illustrated.