On the Estimation of Multiple Random Integrals and U-Statistics: 2079 - Brossura

Major, Péter

 
9783642376160: On the Estimation of Multiple Random Integrals and U-Statistics: 2079
Brossura
ISBN 10: 3642376169 ISBN 13: 9783642376160
Casa editrice: Springer, 2013

Sinossi

This work starts with the study of those limit theorems in probability theory for which classical methods do not work. In many cases some form of linearization can help to solve the problem, because the linearized version is simpler. But in order to apply such a method we have to show that the linearization causes a negligible error. The estimation of this error leads to some important large deviation type problems, and the main subject of this work is their investigation. We provide sharp estimates of the tail distribution of multiple integrals with respect to a normalized empirical measure and so-called degenerate U-statistics and also of the supremum of appropriate classes of such quantities. The proofs apply a number of useful techniques of modern probability that enable us to investigate the non-linear functionals of independent random variables.
This lecture note yields insights into these methods, and may also be useful for those who only want some new tools to help them prove limit theorems when standard methods are not a viable option.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Dalla quarta di copertina

This work starts with the study of those limit theorems in probability theory for which classical methods do not work. In many cases some form of linearization can help to solve the problem, because the linearized version is simpler. But in order to apply such a method we have to show that the linearization causes a negligible error. The estimation of this error leads to some important large deviation type problems, and the main subject of this work is their investigation. We provide sharp estimates of the tail distribution of multiple integrals with respect to a normalized empirical measure and so-called degenerate U-statistics and also of the supremum of appropriate classes of such quantities. The proofs apply a number of useful techniques of modern probability that enable us to investigate the non-linear functionals of independent random variables.
This lecture note yields insights into these methods, and may also be useful for those who only want some new tools to help them prove limit theorems when standard methods are not a viable option.

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

Editore
Springer
Data di pubblicazione
2013
Lingua
Inglese
ISBN 10 
3642376169
ISBN 13 
9783642376160
Rilegatura
Copertina flessibile
Numero di pagine
304
Contatto del produttore
ProductSafety@springernature.com
ProductSafety@springernature.com

Poststr. 9
Darmstadt
64293
Germania

Altre edizioni note dello stesso titolo

9783642376184: On the Estimation of Multiple Random Integrals and U-Statistics

Edizione in evidenza

ISBN 10:  3642376185 ISBN 13:  9783642376184
Casa editrice: Springer, 2013
Brossura