High Dimensional Probability III

by Hoffmann-Jorgensen, Jorgen; Marcus, Michael B.; Wellner, Jon A.; Wellner, Jon A.

• ISBN13: 9783764321871
• ISBN10: 3764321873
• Format: Hardcover
• Copyright: 2004-03-01
• Publisher: Birkhauser

Summary

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.

Table of Contents

Preface	vii
I. Measures on General Spaces and Inequalities
J. Hoffmann-Jorgensen
Stochastic inequalities and perfect independence	3	(32)
Jun Kawabe
Prokhorov-LeCam-Varadarajan's compactness criteria for vector measures on metric spaces	35	(8)
A.V. Uglanov
On measures in locally convex spaces	43	(14)
II. Gaussian Processes
Paul Deheuvels and Guennady Martgnor
Karhunen-Loeve expansions for weiglited Wiener processes and Brownian bridges via Bessel functions	57	(38)
Xavier Ferrique
Extension du theoreme de Cameron-Martin aux translations aleatoires. II. Integrabilite des densites	95	(10)
III. Limit Theorems
Vladimir Dobric and Lisa Marano
Rates of convergence for Levy's modulus of continuity and Hinchin's law of the iterated logarithm	105	(6)
Stanislaw Kwapien, Rafal Latala, Krzysztof Oleszkiewicz and Joel Zinn
On the limit set in the law of the iterated logarithm for U-statistics of order two	111	(16)
Andre Mas and Ludovic Menneteau
Perturbation approach applied to the asymptotic study of random operators	127	(8)
David M. Mason
A uniform functional law of the logarithm for a local Gaussian process	135	(18)
Olzmjon Sh. Sharipov
Strong limit theorems for mixing random variables with values in Hilbert space and their applications	153	(24)
IV. Local Times
R. Ghomrasni and G. Peskir
Local time-space calculus and extensions of Ito's formula	177	(16)
Michael B. Marcus
Local times on curves and surfaces	193	(12)
V. Large and Small Deviations
Miguel A. Arcones
Large deviations of empirical processes	205	(20)
Xia Chen and Wenbo V. Li
Small deviation estimates for some additive processes	225	(16)
VI. Density Estimation
Evarist Gine, Vladimir Koltchinskii and Lyudmila Sakhanenko
Convergence in distribution of self-normalized sup-norms of kernel density estimators	241	(14)
Andrei Yu. Zaitsev
Estimates of the rate of approximation in the CLT for L1-norm of density estimators	255	(40)
VII. Statistics via Empirical Process Theory
R.M. Dudley
Statistical nearly universal Glivenko-Cantelli classes	295	(18)
Peter Gaenssler and Daniel Rost
Smoothed empirical processes and the bootstrap	313	(8)
Jon A. Wellner and Vladimir Koltchinskii
A note on the asymptotic distribution of Berk-Jones type statistics under the null hypothesis	321	(12)
Dragan Radulovic
A note on the smoothed bootstrap	333