Optimal inference for the mean of random functions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909580090408960 |
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| author | Kassi, Omar Patilea, Valentin |
| author_facet | Kassi, Omar Patilea, Valentin |
| contents | We study estimation and inference for the mean of real-valued random functions defined on a hypercube. The independent random functions are observed on a discrete, random subset of design points, possibly with heteroscedastic noise. We propose a novel optimal-rate estimator based on Fourier series expansions and establish a sharp non-asymptotic error bound in $L^2-$norm. Additionally, we derive a non-asymptotic Gaussian approximation bound for our estimated Fourier coefficients. Pointwise and uniform confidence sets are constructed. Our approach is made adaptive by a plug-in estimator for the Hölder regularity of the mean function, for which we derive non-asymptotic concentration bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11025 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal inference for the mean of random functions Kassi, Omar Patilea, Valentin Statistics Theory Methodology We study estimation and inference for the mean of real-valued random functions defined on a hypercube. The independent random functions are observed on a discrete, random subset of design points, possibly with heteroscedastic noise. We propose a novel optimal-rate estimator based on Fourier series expansions and establish a sharp non-asymptotic error bound in $L^2-$norm. Additionally, we derive a non-asymptotic Gaussian approximation bound for our estimated Fourier coefficients. Pointwise and uniform confidence sets are constructed. Our approach is made adaptive by a plug-in estimator for the Hölder regularity of the mean function, for which we derive non-asymptotic concentration bounds. |
| title | Optimal inference for the mean of random functions |
| topic | Statistics Theory Methodology |
| url | https://arxiv.org/abs/2504.11025 |