2 problems

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Asymptotic equivalence of random-design regression and Gaussian white noise
Let $X_1,\ldots,X_n$ be independent and uniformly distributed on the sphere $\mathbb{S}^d$ , let $\varepsilon_1,\ldots,\varepsilon_n$ be independent standard Gaussian variables inde…
Conjectureopenasymptotic-equivalence nonparametric-regression random-designarXiv posted 2 days ago
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Extension of minimax goodness-of-fit results to unknown product design densities
Unknown-design extension conjecture. Subject to additional constraints similar to those in the cited work, the main results established in Theorems … should extend to unknown produ…
Conjectureopengoodness-of-fit-testing nonparametric-regression random-designarXiv posted 2 days ago

Asymptotic equivalence of random-design regression and Gaussian white noise