Relationships between Donsker classes and Sobolev spaces

DOI10.1007/BF00532737zbMath0525.60008MaRDI QIDQ3038271

David J. Marcus

Publication date: 1985

Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)

zbMATH Keywords

Sobolev spaceDonsker class

Mathematics Subject Classification ID

Probability theory on linear topological spaces (60B11)

Related Items (4)

On the optimal estimation of probability measures in weak and strong topologies ⋮ Bracketing metric entropy rates and empirical central limit theorems for function classes of Besov- and Sobolev-type ⋮ Uniform central limit theorems for kernel density estimators ⋮ Unnamed Item

Cites Work

• The addition formula for the eigenfunctions of the Laplacian
• Invariant tests for uniformity on compact Riemannian manifolds based on Sobolev norms
• Central limit theorems for empirical measures
• The sizes of compact subsets of Hilbert space and continuity of Gaussian processes
• Invariance principles for sums of Banach space valued random elements and empirical processes
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