Overview
- Includes new coverage of Glivenko-Cantelli preservation theorems & new applications in statistics
- Covers a range of applications in statistics including rates of convergence of estimators
- Presents a thorough treatment of stochastic convergence in its various forms
Part of the book series: Springer Series in Statistics (SSS)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
About this book
This second edition includes many of the new developments in the field since publication of the first edition in 1996: Glivenko-Cantelli preservation theorems; new bounds on expectations ofsuprema of empirical processes; new bounds on covering numbers for various function classes; generic chaining; definitive versions of concentration bounds; and new applications in statistics including penalized M-estimation, the lasso, classification, and support vector machines. The approximately 200 additional pages also round out classical subjects, including chapters on weak convergence in Skorokhod space, on stable convergence, and on processes based on pseudo-observations.
Keywords
Table of contents (3 chapters)
-
Front Matter
-
Back Matter
Authors and Affiliations
About the authors
A.W. van der Vaart is a Professor of Statistics at Delft University, the Netherlands. He earned his Ph.D. in Mathematics from Leiden University. His research interests are in statistics and probability, as mathematical disciplines and in their applications to other sciences, with an emphasis on statistical models with large parameter spaces. He is a member of the Royal Netherlands Academy of Arts and Sciences and recipient of the Spinoza prize. He is a former president of the Netherlands Society for Statistics and Operations Research and served the national and international mathematical and statistical communities in various capacities. He has authored or co-authored eight books, one awarded with the DeGroot prize.
Jon A. Wellner is a Professor of Statistics at the University of Washington, Seattle. He earned his Ph.D. in Statistics from the University of Washington. His research interests include uses of large sample theory in statistics, theory of empirical processes and probability in high-dimensional settings, and efficient estimation for semiparametric models. He is also interested in statistical methods under shape constraints. He is a member of the American Association for the Advancement of Science, the Institute of Mathematical Statistics, the Bernoulli Society, and the International Statistical Institute, as well as the Mathematical Association of America, the Society for Industrial and Applied Mathematics, and the American Mathematical Society. He is a past President of the Institute of Mathematical Statistics, has served as an editor or co-editor of the Annals of Statistics and Statistical Science, and has co-authored or co-edited ten books.
Bibliographic Information
Book Title: Weak Convergence and Empirical Processes
Book Subtitle: With Applications to Statistics
Authors: A. W. van der Vaart, Jon A. Wellner
Series Title: Springer Series in Statistics
DOI: https://doi.org/10.1007/978-3-031-29040-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-29038-1Published: 12 July 2023
eBook ISBN: 978-3-031-29040-4Published: 11 July 2023
Series ISSN: 0172-7397
Series E-ISSN: 2197-568X
Edition Number: 2
Number of Pages: XVII, 679
Topics: Applied Statistics, Statistical Theory and Methods, Bayesian Inference