Sharp Debiasing for Smooth Functional Estimation in Banach Spaces
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912997651251200 |
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| author | Chang, Woonyoung Kuchibhotla, Arun Kumar |
| author_facet | Chang, Woonyoung Kuchibhotla, Arun Kumar |
| contents | This paper studies the estimation of smooth functionals $f(θ)$ of a mean parameter $θ= \mathbb{E}_P[W]$ for a distribution $P$ on a general Banach space. We propose a cross-fitted estimator based on a single sample splitting and establish non-asymptotic moment bounds and Berry--Esséen bounds for both $m$-smooth and infinitely smooth functionals under the finite moment assumptions. Our framework is applied to precision matrix estimation and the inference of projection parameters in high-dimensional regression. In these Euclidean settings, the proposed estimators achieve asymptotic normality under the dimension regime $d \log^2(en) = o(n)$ without requiring any structural assumptions (e.g., sparsity). We discuss computational relaxations that enables polynomial-time implementation for a range of matrix functionals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01470 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp Debiasing for Smooth Functional Estimation in Banach Spaces Chang, Woonyoung Kuchibhotla, Arun Kumar Statistics Theory Methodology This paper studies the estimation of smooth functionals $f(θ)$ of a mean parameter $θ= \mathbb{E}_P[W]$ for a distribution $P$ on a general Banach space. We propose a cross-fitted estimator based on a single sample splitting and establish non-asymptotic moment bounds and Berry--Esséen bounds for both $m$-smooth and infinitely smooth functionals under the finite moment assumptions. Our framework is applied to precision matrix estimation and the inference of projection parameters in high-dimensional regression. In these Euclidean settings, the proposed estimators achieve asymptotic normality under the dimension regime $d \log^2(en) = o(n)$ without requiring any structural assumptions (e.g., sparsity). We discuss computational relaxations that enables polynomial-time implementation for a range of matrix functionals. |
| title | Sharp Debiasing for Smooth Functional Estimation in Banach Spaces |
| topic | Statistics Theory Methodology |
| url | https://arxiv.org/abs/2604.01470 |