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Author Chen, Louis H
Title An Introduction to Stein's Method
Imprint Singapore : World Scientific Publishing Co Pte Ltd, 2005
©2005
book jacket
Descript 1 online resource (239 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series World Scientific Series On Nonlinear Science Series A ; v.4
World Scientific Series On Nonlinear Science Series A
Note Intro -- CONTENTS -- FOREWORD -- PREFACE -- Stein's method for normal approximation -- Contents -- 1. Introduction -- 2. Fundamentals of Stein's method -- 2.1. Characterization -- 2.2. Properties of the solutions -- 2.3. Construction of the Stein identities -- 3. Normal approximation for smooth functions -- 3.1. Independent random variables -- 3.2. Locally dependent random variables -- 3.3. Exchangeable pairs -- 4. Uniform Berry-Esseen bounds: the bounded case -- 4.1. Independent random variables -- 5. Uniform Berry-Esseen bounds: the independent case -- 5.1. The concentration inequality approach -- 5.2. Proving the Berry-Esseen theorem -- 5.3. A lower bound -- 6. Non-uniform Berry-Esseen bounds: the independent case -- 6.1. A non-uniform concentration inequality -- 6.2. The final result -- 7. Uniform and non-uniform bounds under local dependence -- 8. Appendix -- Acknowledgement -- References -- Stein's method for Poisson and compound Poisson approximation -- Contents -- 1. Introduction -- 2. Poisson approximation -- 2.1. The Stein equation for Po( ) and its solutions -- 2.2. The generator interpretation -- 2.3. Error estimates in Poisson approximation -- 2.4. Monotone couplings -- 2.5. The total mass of a point process -- 2.6. Poisson-Charlier approximation -- 2.7. Poisson approximation for unbounded functions -- 3. Compound Poisson approximation -- 3.1. The CP(π) distrubution -- 3.2. Why compound Poisson approximation? -- 3.3 The Stein equation for CP(π) and its solutions -- 3.4. Error estimates in compound Poisson approximation -- 3.5. The Barbour-Utev version of Stein's method for compound Poisson approximation -- 3.6. Stein's method and Kolmogorov distance -- 3.7. Stein's method for translated signed discrete compound Poisson measure approximation -- 3.8. Compound Poisson approximation via Poisson process approximation
3.9. Compound Poisson approximation on groups -- References -- Stein's method and Poisson process approximation -- Contents -- 1. Introduction -- 2. Poisson point processes -- 2.1. Poisson processes on the real line -- 2.2. Poisson point processes -- 2.3. Characterization of Poisson point processes -- 3. Immigration-death point processes -- 3.1. Immigration-death processes -- 3.2. Spatial immigration-death processes -- 4. Poisson process approximation by coupling -- 4.1. Metrics for quantifying the weak topology in -- 4.2. The metrics for point process approximation -- 4.3. Poisson process approximation using stochastic calculus -- 5. Poisson process approximation via Stein's method -- 5.1. Stein's equation and Stein's factors -- 5.2. One dimensional Poisson process approximation -- 5.3. Poisson process approximation in total variation -- 5.4. Poisson process approximation in the d2-metric -- 6. Applications -- 6.1. Bernoulli process -- 6.2. 2-runs -- 6.3. Matérn hard core process -- 6.4. Networks of queues -- 7. Further developments -- Acknowledgement -- References -- Three general approaches to Stein's method -- Contents -- 1. Introduction -- 2. The generator approach -- 3. Chi-squared distributions -- 4. The weak law of large numbers -- 4.1. Empirical measures -- 4.2. Weak law of large numbers for empirical measures -- 4.3. Mixing random elements -- 4.4. Locally dependent random elements -- 4.5. The size-bias coupling -- 5. Discrete distributions from a Gibbs view point -- 5.1. Bounds on the solution of the Stein equation -- 5.2. The size-bias coupling -- 6. Example: an S-I-R epidemic -- 7. The density approach -- 8. Distributional transformations -- Acknowledgement -- References -- INDEX
Key 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 form
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Chen, Louis H. An Introduction to Stein's Method Singapore : World Scientific Publishing Co Pte Ltd,c2005 9789812562807
Subject Distribution (Probability theory);Approximation theory.;Probabilities
Electronic books
Alt Author Barbour, A.D
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