Automatic and location-adaptive estimation in functional single-index regression
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929225202663424 |
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| author | Novo, Silvia Aneiros, Germán Vieu, Philippe |
| author_facet | Novo, Silvia Aneiros, Germán Vieu, Philippe |
| contents | This paper develops a new automatic and location-adaptive procedure for estimating regression in a Functional Single-Index Model (FSIM). This procedure is based on $k$-Nearest Neighbours ($k$NN) ideas. The asymptotic study includes results for automatically data-driven selected number of neighbours, making the procedure directly usable in practice. The local feature of the $k$NN approach insures higher predictive power compared with usual kernel estimates, as illustrated in some finite sample analysis. As by-product we state as preliminary tools some new uniform asymptotic results for kernel estimates in the FSIM model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14836 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Automatic and location-adaptive estimation in functional single-index regression Novo, Silvia Aneiros, Germán Vieu, Philippe Statistics Theory Methodology 62G05, 62G08 This paper develops a new automatic and location-adaptive procedure for estimating regression in a Functional Single-Index Model (FSIM). This procedure is based on $k$-Nearest Neighbours ($k$NN) ideas. The asymptotic study includes results for automatically data-driven selected number of neighbours, making the procedure directly usable in practice. The local feature of the $k$NN approach insures higher predictive power compared with usual kernel estimates, as illustrated in some finite sample analysis. As by-product we state as preliminary tools some new uniform asymptotic results for kernel estimates in the FSIM model. |
| title | Automatic and location-adaptive estimation in functional single-index regression |
| topic | Statistics Theory Methodology 62G05, 62G08 |
| url | https://arxiv.org/abs/2401.14836 |