2022
DOI: 10.1007/s00440-022-01118-z
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Measure estimation on manifolds: an optimal transport approach

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Cited by 7 publications
(1 citation statement)
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“…For example, if this measure possesses a lower and upper bounded density on some bounded subset of R d , then the rate is known to be n −q/d even if q > d/2 [21]. This rate may even be improved if μ X concentrates on a low-dimensional submanifold of R d [39,16], which is particularly relevant in the UQ context which motivates this study, see Remark 5.3. In order to make the use of our results as flexible as possible, from now on we shall denote by (τ q,d (n)) n≥1 a sequence such that E W q q (μ X , μ Xn ) = O (τ q,d (n)) , and thus…”
Section: Convergence Of μ (K)mentioning
confidence: 92%
“…For example, if this measure possesses a lower and upper bounded density on some bounded subset of R d , then the rate is known to be n −q/d even if q > d/2 [21]. This rate may even be improved if μ X concentrates on a low-dimensional submanifold of R d [39,16], which is particularly relevant in the UQ context which motivates this study, see Remark 5.3. In order to make the use of our results as flexible as possible, from now on we shall denote by (τ q,d (n)) n≥1 a sequence such that E W q q (μ X , μ Xn ) = O (τ q,d (n)) , and thus…”
Section: Convergence Of μ (K)mentioning
confidence: 92%