High-Dimensional Single-Index Models: Link Estimation and Marginal Inference
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910426340524032 |
|---|---|
| author | Sawaya, Kazuma Uematsu, Yoshimasa Imaizumi, Masaaki |
| author_facet | Sawaya, Kazuma Uematsu, Yoshimasa Imaizumi, Masaaki |
| contents | This study proposes a novel method for estimation and hypothesis testing in high-dimensional single-index models. We address a common scenario where the sample size and the dimension of regression coefficients are large and comparable. Unlike traditional approaches, which often overlook the estimation of the unknown link function, we introduce a new method for link function estimation. Leveraging the information from the estimated link function, we propose more efficient estimators that are better aligned with the underlying model. Furthermore, we rigorously establish the asymptotic normality of each coordinate of the estimator. This provides a valid construction of confidence intervals and $p$-values for any finite collection of coordinates. Numerical experiments validate our theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17812 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | High-Dimensional Single-Index Models: Link Estimation and Marginal Inference Sawaya, Kazuma Uematsu, Yoshimasa Imaizumi, Masaaki Statistics Theory Methodology This study proposes a novel method for estimation and hypothesis testing in high-dimensional single-index models. We address a common scenario where the sample size and the dimension of regression coefficients are large and comparable. Unlike traditional approaches, which often overlook the estimation of the unknown link function, we introduce a new method for link function estimation. Leveraging the information from the estimated link function, we propose more efficient estimators that are better aligned with the underlying model. Furthermore, we rigorously establish the asymptotic normality of each coordinate of the estimator. This provides a valid construction of confidence intervals and $p$-values for any finite collection of coordinates. Numerical experiments validate our theoretical results. |
| title | High-Dimensional Single-Index Models: Link Estimation and Marginal Inference |
| topic | Statistics Theory Methodology |
| url | https://arxiv.org/abs/2404.17812 |