Normal Approximation by Stein’s Method

• Κύριοι συγγραφείς: Chen, Louis H.Y (Συγγραφέας), Goldstein, Larry (Συγγραφέας), Shao, Qi-Man (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
• Σειρά: Probability and Its Applications,
• Θέματα: Mathematics.; Probabilities.; Probability Theory and Stochastic Processes.

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 de...

Πίνακας περιεχομένων:

• Preface
• 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.