High Dimensional Probability III
By: edited by Jørgen Hoffmann-Jørgensen, Jon A. Wellner, Michael B. Marcus
Contributors: Wellner, Jon A.; Marcus, Michael B.
Series: Progress in Probability -- 55; Progress in probability -- 55.
Publisher: Birkhäuser Basel; Imprint; Birkhäuser
Published: 2003
Place of publication: Basel
Language: eng
Format: [electronic resource] /
Number of pages: 346
ISBN-13: 9783034880596
Subjects: Mathematics; Distribution (Probability theory); Statistics
Description: The title High Dimensional Probability is used to describe the many tributaries of research on Gaussian processes and probability in Banach spaces that started in the early 1970s. Many of the problems that motivated researchers at that time were solved. But the powerful new tools created for their solution, such as randomization, isoperimetry, concentration of measure, moment and exponential inequalities, chaining, series representations, and decoupling turned out to be applicable to other important areas of probability. They led to significant advances in the study of empirical processes and other topics in theoretical statistics and to a new approach to the study of aspects of Lévy processes and Markov processes in general. The papers in this book reflect these broad categories. They are divided into seven sections: - measures on general spaces and inequalities - Gaussian processes - limit theorems - local times - large and small deviations - density estimation - statistics via empirical process theory.