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Normal Approximation By Stein S Method

Author : Louis H.Y. Chen
ISBN : 3642150071
Genre : Mathematics
File Size : 21. 97 MB
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Since 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.

An Introduction To Stein S Method

Author : A D Barbour
ISBN : 9789814480659
Genre : Mathematics
File Size : 83. 67 MB
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' A common theme in probability theory is the approximation of complicated probability distributions by simpler ones, the central limit theorem being a classical example. Stein's method is a tool which makes this possible in a wide variety of situations. Traditional approaches, for example using Fourier analysis, become awkward to carry through in situations in which dependence plays an important part, whereas Stein's method can often still be applied to great effect. In addition, the method delivers estimates for the error in the approximation, and not just a proof of convergence. Nor is there in principle any restriction on the distribution to be approximated; it can equally well be normal, or Poisson, or that of the whole path of a random process, though the techniques have so far been worked out in much more detail for the classical approximation theorems. This volume of lecture notes provides a detailed introduction to the theory and application of Stein's method, in a form suitable for graduate students who want to acquaint themselves with the method. It includes chapters treating normal, Poisson and compound Poisson approximation, approximation by Poisson processes, and approximation by an arbitrary distribution, written by experts in the different fields. The lectures take the reader from the very basics of Stein's method to the limits of current knowledge. Contents:Normal Approximation (L H Y Chen & Q-M Shao)Poisson and Compound Poisson Approximation (T Erhardsson)Poisson Process Approximation (A-H Xia)Three General Approaches to Stein's Method (G Reinert) Readership: Graduate students of probability. Keywords:Stein''s Method;Probability Approximations;Berry-Esseen;Poisson Approximation;Compound Poisson Approximation;Zero Biasing;Size Biasing;Poisson Process ApproximationKey Features:The first general introduction to the area since Stein's 1986 monographOffers a broad scope: discrete, continuous and process approximationsNew topics such as compound Poisson approximation and polynomial biasing are treated for the first time in book formReviews:“All the lectures have been given by eminent experts working in the area of Stein's method and provide details and unsolved problems along with a list of very useful references. These lectures will be very valuable for both experts and researchers wishing to explore the powerful approximation method proposed by Charles Stein.”Mathematical Reviews '

Normal Approximations With Malliavin Calculus

Author : Ivan Nourdin
ISBN : 9781107017771
Genre : Mathematics
File Size : 21. 25 MB
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This book shows how quantitative central limit theorems can be deduced by combining two powerful probabilistic techniques: Stein's method and Malliavin calculus.

Stein S Method And Applications

Author : A D Barbour
ISBN : 9789814480642
Genre : Mathematics
File Size : 77. 90 MB
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' Stein's startling technique for deriving probability approximations first appeared about 30 years ago. Since then, much has been done to refine and develop the method, but it is still a highly active field of research, with many outstanding problems, both theoretical and in applications. This volume, the proceedings of a workshop held in honour of Charles Stein in Singapore, August 2003, contains contributions from many of the mathematicians at the forefront of this effort. It provides a cross-section of the work currently being undertaken, with many pointers to future directions. The papers in the collection include applications to the study of random binary search trees, Brownian motion on manifolds, Monte-Carlo integration, Edgeworth expansions, regenerative phenomena, the geometry of random point sets, and random matrices. Contents:Zero Biasing in One and Higher Dimensions, and Applications (L Goldstein & G Reinert)Poisson Limit Theorems for the Appearances of Attributes (O Chryssaphinou et al.)Normal Approximation in Geometric Probability (M D Penrose & J E Yukich)Stein's Method, Edgeworth's Expansions and a Formula of Barbour (V Rotar)Stein's Method for Compound Poisson Approximation via Immigration–Death Processes (A Xia)The Central Limit Theorem for the Independence Number for Minimal Spanning Trees in the Unit Square (S Lee & Z Su)Stein's Method, Markov Renewal Point Processes, and Strong Memoryless Time (T Erhardsson)Multivariate Poisson–Binomial Approximation Using Stein's Method (A D Barbour)An Explicit Berry–Esseen Bound for Student's t-Statistic via Stein's Method (Q-M Shao)An Application of Stein's Method to Maxima in Hypercubes (Z D Bai et al.)Exact Expectations of Minimal Spanning Trees for Graphs with Random Edge Weights (J A Fill & J M Steele)Limit Theorems for Spectra of Random Matrices with Martingale Structure (F Götze & A N Tikhomirov)Characterization of Brownian Motion on Manifolds Through Integration by Parts (E P Hsu)On the Asymptotic Distribution of Some Randomized Quadrature Rules (W-L Loh)The Permutation Distribution of Matrix Correlation Statistics (A D Barbour & L H Y Chen)Applications of Stein's Method in the Analysis of Random Binary Search Trees (L Devroye) Readership: Researchers and graduate students in probability. Keywords:Stein''s Method;Probability Approximations;Berry-Esseen;Poisson Approximation;Compound Poisson Approximation;Zero Biasing;Binary Search Trees;Edgeworth Expansions;Brownian Motion;Monte-Carlo Integration;Regenerative Phenomena;Geometrical Probability;Random Matrices;Minimal Spanning TreeKey Features:Cross-section of topics of current interest in the area of Steins' method'

Probability Approximations And Beyond

Author : Andrew Barbour
ISBN : 9781461419655
Genre : Mathematics
File Size : 41. 20 MB
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In June 2010, a conference, Probability Approximations and Beyond, was held at the National University of Singapore (NUS), in honor of pioneering mathematician Louis Chen. Chen made the first of several seminal contributions to the theory and application of Stein’s method. One of his most important contributions has been to turn Stein’s concentration inequality idea into an effective tool for providing error bounds for the normal approximation in many settings, and in particular for sums of random variables exhibiting only local dependence. This conference attracted a large audience that came to pay homage to Chen and to hear presentations by colleagues who have worked with him in special ways over the past 40+ years. The papers in this volume attest to how Louis Chen’s cutting-edge ideas influenced and continue to influence such areas as molecular biology and computer science. He has developed applications of his work on Poisson approximation to problems of signal detection in computational biology. The original papers contained in this book provide historical context for Chen’s work alongside commentary on some of his major contributions by noteworthy statisticians and mathematicians working today.

Random Discrete Structures

Author : David Aldous
ISBN : 9781461207191
Genre : Mathematics
File Size : 32. 85 MB
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The articles in this volume present the state of the art in a variety of areas of discrete probability, including random walks on finite and infinite graphs, random trees, renewal sequences, Stein's method for normal approximation and Kohonen-type self-organizing maps. This volume also focuses on discrete probability and its connections with the theory of algorithms. Classical topics in discrete mathematics are represented as are expositions that condense and make readable some recent work on Markov chains, potential theory and the second moment method. This volume is suitable for mathematicians and students.

Stein S Method

Author : Persi Diaconis
ISBN : 0940600625
Genre : Mathematics
File Size : 78. 87 MB
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"These papers were presented and developed as expository talks at a summer-long workshop on Stein's method at Stanford's Department of Statistics in 1998."--P. iii.

Modelos Estoc?sticos

Author : José María González Barrios
ISBN : 9683676553
Genre : Probabilities
File Size : 70. 98 MB
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Analysis Of Variations For Self Similar Processes

Author : Ciprian Tudor
ISBN : 9783319009360
Genre : Mathematics
File Size : 57. 53 MB
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Self-similar processes are stochastic processes that are invariant in distribution under suitable time scaling, and are a subject intensively studied in the last few decades. This book presents the basic properties of these processes and focuses on the study of their variation using stochastic analysis. While self-similar processes, and especially fractional Brownian motion, have been discussed in several books, some new classes have recently emerged in the scientific literature. Some of them are extensions of fractional Brownian motion (bifractional Brownian motion, subtractional Brownian motion, Hermite processes), while others are solutions to the partial differential equations driven by fractional noises. In this monograph the author discusses the basic properties of these new classes of self-similar processes and their interrelationship. At the same time a new approach (based on stochastic calculus, especially Malliavin calculus) to studying the behavior of the variations of self-similar processes has been developed over the last decade. This work surveys these recent techniques and findings on limit theorems and Malliavin calculus.

Mathematical Reviews

Author :
ISBN : UVA:X006180632
Genre : Mathematics
File Size : 53. 96 MB
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Analele Universit??ii Bucure?ti

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ISBN : STANFORD:36105123834785
Genre : Computer science
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Proceedings Of The National Academy Of Sciences Of The United States Of America

Author : National Academy of Sciences (U.S.)
ISBN : UOM:39015047926756
Genre : Science
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Bulletin New Series Of The American Mathematical Society

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ISBN : UCSD:31822036949493
Genre : Mathematics
File Size : 78. 63 MB
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The Annals Of Applied Probability

Author :
ISBN : UCSD:31822020210142
Genre : Probabilities
File Size : 31. 93 MB
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Probability A Graduate Course

Author : Allan Gut
ISBN : 0387273328
Genre : Mathematics
File Size : 70. 55 MB
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This textbook on the theory of probability starts from the premise that rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to cover a number of subjects in detail, including chapters on inequalities, characteristic functions and convergence. This is followed by explanations of the three main subjects in probability: the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales.

The Journal Of Computational Finance

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ISBN : CORNELL:31924083439137
Genre : Finance
File Size : 50. 35 MB
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Stochastic Geometry Spatial Statistics And Random Fields

Author : Volker Schmidt
ISBN : 9783319100647
Genre : Mathematics
File Size : 35. 33 MB
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This volume is an attempt to provide a graduate level introduction to various aspects of stochastic geometry, spatial statistics and random fields, with special emphasis placed on fundamental classes of models and algorithms as well as on their applications, e.g. in materials science, biology and genetics. This book has a strong focus on simulations and includes extensive codes in Matlab and R which are widely used in the mathematical community. It can be seen as a continuation of the recent volume 2068 of Lecture Notes in Mathematics, where other issues of stochastic geometry, spatial statistics and random fields were considered with a focus on asymptotic methods.

Almost Everywhere Convergence Ii

Author : Alexandra Bellow
ISBN : UCAL:B4406723
Genre : Mathematics
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Almost Everywhere Convergence II.

Selected Aspects Of Fractional Brownian Motion

Author : Ivan Nourdin
ISBN : 9788847028234
Genre : Mathematics
File Size : 65. 17 MB
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Fractional Brownian motion (fBm) is a stochastic process which deviates significantly from Brownian motion and semimartingales, and others classically used in probability theory. As a centered Gaussian process, it is characterized by the stationarity of its increments and a medium- or long-memory property which is in sharp contrast with martingales and Markov processes. FBm has become a popular choice for applications where classical processes cannot model these non-trivial properties; for instance long memory, which is also known as persistence, is of fundamental importance for financial data and in internet traffic. The mathematical theory of fBm is currently being developed vigorously by a number of stochastic analysts, in various directions, using complementary and sometimes competing tools. This book is concerned with several aspects of fBm, including the stochastic integration with respect to it, the study of its supremum and its appearance as limit of partial sums involving stationary sequences, to name but a few. The book is addressed to researchers and graduate students in probability and mathematical statistics. With very few exceptions (where precise references are given), every stated result is proved.

Encyclopedia Of Statistical Sciences Volume 13

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ISBN : 0471744050
Genre : Mathematics
File Size : 89. 39 MB
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Countless professionals and students who use statistics in their work rely on the multi-volume Encyclopedia of Statistical Sciences as a superior and unique source of information on statistical theory, methods, and applications. This new edition (available in both print and on-line versions) is designed to bring the encyclopedia in line with the latest topics and advances made in statistical science over the past decade--in areas such as computer-intensive statistical methodology, genetics, medicine, the environment, and other applications. Written by over 600 world-renowned experts (including the editors), the entries are self-contained and easily understood by readers with a limited statistical background. With the publication of this second edition in 16 printed volumes, the Encyclopedia of Statistical Sciences retains its position as a cutting-edge reference of choice for those working in statistics, biostatistics, quality control, economics, sociology, engineering, probability theory, computer science, biomedicine, psychology, and many other areas. The Encyclopedia of Statistical Sciences is also available as a 16 volume A to Z set. Volume 13: St-To.

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