| Descript |
1 online resource (239 pages) |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
World Scientific Series On Nonlinear Science Series A ; v.4 |
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World Scientific Series On Nonlinear Science Series A
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| 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 |
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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 |
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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 |
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Description based on publisher supplied metadata and other sources |
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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
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| Subject |
Distribution (Probability theory);Approximation theory.;Probabilities
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Electronic books
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| Alt Author |
Barbour, A.D
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