Weak Convergence and Empirical Processes
With Applications to Statistics
2nd Edition
Published on 11. July 2023
XVII, 679 pages
978-3-031-29040-4 (ISBN)
Description
This book provides an account of weak convergence theory, empirical processes, and their application to a wide variety of problems in statistics. The first part of the book presents a thorough treatment of stochastic convergence in its various forms. Part 2 brings together the theory of empirical processes in a form accessible to statisticians and probabilists. In Part 3, the authors cover a range of applications in statistics including rates of convergence of estimators; limit theorems for M- and Z-estimators; the bootstrap; the functional delta-method and semiparametric estimation. Most of the chapters conclude with "problems and complements." Some of these are exercises to help the reader's understanding of the material, whereas others are intended to supplement the text.
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.
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.
More details
Series
Edition
2nd ed. 2023
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
XVII, 679 p.
File size
8,78 MB
ISBN-13
978-3-031-29040-4 (9783031290404)
DOI
10.1007/978-3-031-29040-4
Schweitzer Classification
Other editions
Additional editions
A. W. van der Vaart | Jon A. Wellner
Weak Convergence and Empirical Processes
With Applications to Statistics
Book
07/2023
2nd Edition
Springer
€149.79
Shipment within 15-20 days
Persons
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.
Content
Preface.- Reading Guide.- Part I: Stochastic Convergence.- Part 2: Empirical Processes.- Part 3: Statistical Applications.- Appendix.- References.- Author Index.- Subject Index.- List of Symbols.
