The DOI matches its Crossref record; 94 of the 94 references it cites were found in a registry or an index.
Uniform Central Limit Theorems
Abstract
This book shows how the central limit theorem for independent, identically distributed random variables with values in general, multidimensional spaces, holds uniformly over some large classes of functions. The author, an acknowledged expert, gives a thorough treatment of the subject, including several topics not found in any previous book, such as the Fernique-Talagrand majorizing measure theorem for Gaussian processes, an extended treatment of Vapnik-Chervonenkis combinatorics, the Ossiander L2 bracketing central limit theorem, the Giné-Zinn bootstrap central limit theorem in probability, the Bronstein theorem on approximation of convex sets, and the Shor theorem on rates of convergence over lower layers. Other results of Talagrand and others are surveyed without proofs in separate sections. Problems are included at the end of each chapter so the book can be used as an advanced text. The book will interest mathematicians working in probability, mathematical statisticians and computer scientists working in computer learning theory.
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Cites
An Introduction to the Bootstrap
Efron, B., & Tibshirani, R. J. (1994) · doi:10.1201/9780429246593 · Cited by 40,500
An introduction to probability theory and its applications
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Bootstrap methods: another look at the jackknife
Efron, B. (1979) · The Annals of Statistics · doi:10.1214/aos/1176344552 · Cited by 17,602
Convergence of Probability Measures
Billingsley, P. (1999) · Wiley Series in Probability and Statistics · doi:10.1002/9780470316962 · Cited by 13,910
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Probability Inequalities for sums of Bounded Random Variables
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Introduction to Fourier Analysis on Euclidean Spaces.
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Weak Convergence and Empirical Processes
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On the mathematical foundations of theoretical statistics
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Cited by
Concentration Inequalities: A Nonasymptotic Theory of Independence
Boucheron, S., Lugosi, G., & Massart, P. (2013) · doi:10.1093/acprof:oso/9780199535255.001.0001 · Cited by 1,768
Concentration Inequalities and Model Selection
(2007) · Lecture Notes in Mathematics · doi:10.1007/978-3-540-48503-2 · Cited by 744
Consistency of spectral clustering
von Luxburg, U., Belkin, M., & Bousquet, O. (2008) · The Annals of Statistics · doi:10.1214/009053607000000640 · Cited by 540
An Introduction to Computational Stochastic PDEs
Lord, G. J., Powell, C. E., & Shardlow, T. (2014) · Cambridge University Press eBooks · doi:10.1017/cbo9781139017329 · Cited by 537
Introduction to Statistical Learning Theory
Bousquet, O., Boucheron, S., & Lugosi, G. (2004) · Lecture Notes in Computer Science · doi:10.1007/978-3-540-28650-9_8 · Cited by 503
Metadata
- Authors
- Dudley, R. M.
- Venue
- Cambridge University Press eBooks
- Publisher
- Cambridge University Press
- Published
- 1999-07-28
- OpenAlex
- W1507545330
- Cited by
- 785
- References
- 94
- FWCI
- 3.80
- Type
- book
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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