Doukhan, P.; Gamboa, F. Superresolution rates in Prokhorov metric. (English) Zbl 0861.60005 Can. J. Math. 48, No. 2, 316-329 (1996). Summary: Consider the problem of recovering a probability measure supported by a compact subset \(U\) of \(\mathbb{R}^m\) when the available measurements concern only some of its \(\Phi\)-moments (\(\Phi\) being an \(\mathbb{R}^k\) valued continuous function on \(U\)). When the true \(\Phi\)-moment \(c\) lies on the boundary of the convex hull of \(\Phi(U)\), generalizing the results of the second author and E. Gassiat [SIAM J. Math. Anal. 27, No. 4, 1129-1152 (1996)], we construct a small set \(R_{\alpha,\delta(\varepsilon)}\) such that any probability measure \(\mu\) satisfying \(|\int_U \Phi(x)d\mu(x)-c|\leq\varepsilon\) is almost concentrated on \(R_{\alpha,\delta(\varepsilon)}\). When \(\Phi\) is a pointwise \(T\)-system (extension of \(T\)-systems), the study of the set \(R_{\alpha,\delta(\varepsilon)}\) leads to the evaluation of the Prokhorov radius of the set \(\{\mu: |\int_U \Phi(x)d\mu(x)-c|\leq \varepsilon\}\). Cited in 7 Documents MSC: 60A10 Probabilistic measure theory 43A07 Means on groups, semigroups, etc.; amenable groups 62A01 Foundations and philosophical topics in statistics Keywords:probability measure; Prokhorov radius PDFBibTeX XMLCite \textit{P. Doukhan} and \textit{F. Gamboa}, Can. J. Math. 48, No. 2, 316--329 (1996; Zbl 0861.60005) Full Text: DOI