000			02910nam a22003618i 4500
001			CR9780511665622
003			UkCbUP
005			20200124160242.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			091217s1999||||enk o ||1 0|eng|d
020			_a9780511665622 (ebook)
020			_z9780521461023 (hardback)
020			_z9780521052214 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA273.67 _b.D84 1999
082	0	0	_a519.2 _221
100	1		_aDudley, R. M. _q(Richard M.), _eauthor.
245	1	0	_aUniform central limit theorems / _cR.M. Dudley.
264		1	_aCambridge : _bCambridge University Press, _c1999.
300			_a1 online resource (xiv, 436 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge studies in advanced mathematics ; _v63
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_a1. Introduction: Donsker's theorem, metric entropy, and inequalitites 2. Gaussian measures and processes 3. Foundations of uniform central limit theorems: Donsker classes 4. Vapnik-Cervonenkis combinatorics 5. Measurability 6. Limit theorems for Vapnik-Cervonenkis classes and Koltchinskii-Pollard entropy 7. Metric entropy, with inclusion and bracketing 8. Approximation of functions and sets 9. Sums in general Banach spaces and invariance 10. Universal and uniform central limit theorems 11. The two-sample case, the bootstrap, and confidence sets 12. Classes of sets or functions too large for central limit theorems.
520			_aThis 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.
650		0	_aCentral limit theorem.
776	0	8	_iPrint version: _z9780521461023
830		0	_aCambridge studies in advanced mathematics ; _v63.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511665622
999			_c518604 _d518602