UNIFORM CENTRAL LIMIT THEOREMS (Cambridge Studies in Advanced Mathematics 63) By R. M. D UDLEY : 436pp., £55.00, ISBN 0-521-46102-2 (Cambridge University Press, 1999).
By E. Berger. 2001
126 citations recorded by the source corpus.
Subfields: Computational Theory and Mathematics
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In Computational Theory and Mathematics
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Citations in the corpus
- Minimax Estimation of Kernel Mean Embeddings (2016, background): “An ǫ-covering number N(A, ǫ) of A is the minimal number of balls of radius ǫ needed to cover A. Packing numbers are lower bounded by the covering numbers (Dudley, 1999, Theorem 1.2.1): N(A, ǫ) ≤M(A, ǫ).”
- TESTING REGRESSION MONOTONICITY IN ECONOMETRIC MODELS (2012, methodology): “The difficulty here is that the processes underlying the test statistic do not have an asymptotic equicontinuity property, and so classical functional central limit theorems, as presented for example in van der Vaart and Wellner (1996) and Dudley (1999), do not apply. One of the main contributions o”
- Learning theory: stability is sufficient for generalization and necessary and sufficient for consistency of empirical risk minimization (2006, methodology): “The key ingredient in our definitions of stability given above is some measure on | f S − f Si | , e.g., a measure of the difference between the error made by the predictor obtained by using ERM on the training set S vs. the error of the predictor obtained from a slightly perturbed training set S i .”
- A Few Notes on Statistical Learning Theory (2002, methodology): “One can turn to [5] for a more detailed introduction, or to [34, 8] for a complete and rigorous analysis.”
- Asymptotics and optimal bandwidth selection for highest density region estimation (2010, methodology): “Here, the final inequality is an application of Corollary 2.2 of Giné and Guillou (2002) (a consequence of Talagrand’s inequality) to the Vapnik– Cervonenkis class of functions {K((x − ·)/h) :x ∈ R, h > 0} [cf. Dudley (1999), Theorems 4.2.1 and 4.2.4].”
- Regularization in kernel learning (2010, methodology): “This is a generalization of Dudley’s entropy integral (see for example [9, 29]), used in the study of Gaussian processes.”