Asymptotic equivalence for nonparametric additive regression
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917266511101952 |
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| author | Jirak, Moritz Meister, Alexander Rohde, Angelika |
| author_facet | Jirak, Moritz Meister, Alexander Rohde, Angelika |
| contents | We prove asymptotic equivalence of nonparametric additive regression and an appropriate Gaussian white noise experiment in which a multidimensional shifted Wiener process is observed, whose dimension equals the number of additive components. The shift depends on the additive components of the regression function and solely the one- and two-dimensional marginal distributions of the covariates via an explicitly specified bounded but non-compact linear operator~$Γ$. The number of additive components $d$ is allowed to increase moderately with respect to the sample size. In the special case of pairwise independent components of the covariates, the white noise model decomposes into $d$ independent univariate processes. Moreover, we study approximation in some semiparametric setting where $Γ$ splits into a multiplication operator and an asymptotically negligible Hilbert-Schmidt operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10274 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic equivalence for nonparametric additive regression Jirak, Moritz Meister, Alexander Rohde, Angelika Statistics Theory 62G08, 62B15 We prove asymptotic equivalence of nonparametric additive regression and an appropriate Gaussian white noise experiment in which a multidimensional shifted Wiener process is observed, whose dimension equals the number of additive components. The shift depends on the additive components of the regression function and solely the one- and two-dimensional marginal distributions of the covariates via an explicitly specified bounded but non-compact linear operator~$Γ$. The number of additive components $d$ is allowed to increase moderately with respect to the sample size. In the special case of pairwise independent components of the covariates, the white noise model decomposes into $d$ independent univariate processes. Moreover, we study approximation in some semiparametric setting where $Γ$ splits into a multiplication operator and an asymptotically negligible Hilbert-Schmidt operator. |
| title | Asymptotic equivalence for nonparametric additive regression |
| topic | Statistics Theory 62G08, 62B15 |
| url | https://arxiv.org/abs/2602.10274 |