000 03204nam a22004815i 4500
001 978-3-642-15007-4
003 DE-He213
005 20140220083746.0
007 cr nn 008mamaa
008 101013s2011 gw | s |||| 0|eng d
020 _a9783642150074
_9978-3-642-15007-4
024 7 _a10.1007/978-3-642-15007-4
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aChen, Louis H.Y.
_eauthor.
245 1 0 _aNormal Approximation by Stein’s Method
_h[electronic resource] /
_cby Louis H.Y. Chen, Larry Goldstein, Qi-Man Shao.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2011.
300 _aXII, 408 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProbability and Its Applications,
_x1431-7028
505 0 _aPreface -- 1.Introduction -- 2.Fundamentals of Stein's Method -- 3.Berry-Esseen Bounds for Independent Random Variables -- 4.L^1 Bounds -- 5.L^1 by Bounded Couplings -- 6 L^1: Applications -- 7.Non-uniform Bounds for Independent Random Variables -- 8.Uniform and Non-uniform Bounds under Local Dependence -- 9.Uniform and Non-Uniform Bounds for Non-linear Statistics -- 10.Moderate Deviations -- 11.Multivariate Normal Approximation -- 12.Discretized normal approximation -- 13.Non-normal Approximation -- 14.Extensions -- References -- Author Index -- Subject Index -- Notation.
520 _aSince its introduction in 1972, Stein’s method has offered a completely novel way of evaluating the quality of normal approximations. Through its characterizing equation approach, it is able to provide approximation error bounds in a wide variety of situations, even in the presence of complicated dependence. Use of the method thus opens the door to the analysis of random phenomena arising in areas including statistics, physics, and molecular biology. Though Stein's method for normal approximation is now mature, the literature has so far lacked a complete self contained treatment. This volume contains thorough coverage of the method’s fundamentals, includes a large number of recent developments in both theory and applications, and will help accelerate the appreciation, understanding, and use of Stein's method by providing the reader with the tools needed to apply it in new situations. It addresses researchers as well as graduate students in Probability, Statistics and Combinatorics.
650 0 _aMathematics.
650 0 _aDistribution (Probability theory).
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
700 1 _aGoldstein, Larry.
_eauthor.
700 1 _aShao, Qi-Man.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642150067
830 0 _aProbability and Its Applications,
_x1431-7028
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-15007-4
912 _aZDB-2-SMA
999 _c107016
_d107016