Robust Nonparametric Regression for Compositional Data: the Simplicial--Real case
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913850402537472 |
|---|---|
| author | Bianco, Ana M. Boente, Graciela González--Manteiga, Wenceslao Sampedro, Francisco Gude Pérez--González, Ana |
| author_facet | Bianco, Ana M. Boente, Graciela González--Manteiga, Wenceslao Sampedro, Francisco Gude Pérez--González, Ana |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12924 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Robust Nonparametric Regression for Compositional Data: the Simplicial--Real case Bianco, Ana M. Boente, Graciela González--Manteiga, Wenceslao Sampedro, Francisco Gude Pérez--González, Ana Methodology 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. |
| title | Robust Nonparametric Regression for Compositional Data: the Simplicial--Real case |
| topic | Methodology |
| url | https://arxiv.org/abs/2405.12924 |