Asymptotic Equivalence for Nonparametric Regression
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909434203078656 |
|---|---|
| author | Grama, Ion Nussbaum, Michael |
| author_facet | Grama, Ion Nussbaum, Michael |
| contents | We consider a nonparametric model $\mathcal{E}^{n},$ generated by independent observations $X_{i},$ $i=1,...,n,$ with densities $p(x,θ_{i}),$ $i=1,...,n,$ the parameters of which $θ_{i}=f(i/n)\in Θ$ are driven by the values of an unknown function $f:[0,1]\rightarrow Θ$ in a smoothness class. The main result of the paper is that, under regularity assumptions, this model can be approximated, in the sense of the Le Cam deficiency pseudodistance, by a nonparametric Gaussian shift model $Y_{i}=Γ(f(i/n))+\varepsilon _{i},$ where $\varepsilon_{1},...,\varepsilon _{n}$ are i.i.d. standard normal r.v.'s, the function $Γ(θ):Θ\rightarrow \mathrm{R}$ satisfies $Γ^{\prime}(θ)=\sqrt{I(θ)}$ and $I(θ)$ is the Fisher information corresponding to the density $p(x,θ).$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14800 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic Equivalence for Nonparametric Regression Grama, Ion Nussbaum, Michael Statistics Theory We consider a nonparametric model $\mathcal{E}^{n},$ generated by independent observations $X_{i},$ $i=1,...,n,$ with densities $p(x,θ_{i}),$ $i=1,...,n,$ the parameters of which $θ_{i}=f(i/n)\in Θ$ are driven by the values of an unknown function $f:[0,1]\rightarrow Θ$ in a smoothness class. The main result of the paper is that, under regularity assumptions, this model can be approximated, in the sense of the Le Cam deficiency pseudodistance, by a nonparametric Gaussian shift model $Y_{i}=Γ(f(i/n))+\varepsilon _{i},$ where $\varepsilon_{1},...,\varepsilon _{n}$ are i.i.d. standard normal r.v.'s, the function $Γ(θ):Θ\rightarrow \mathrm{R}$ satisfies $Γ^{\prime}(θ)=\sqrt{I(θ)}$ and $I(θ)$ is the Fisher information corresponding to the density $p(x,θ).$ |
| title | Asymptotic Equivalence for Nonparametric Regression |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2412.14800 |