Lectures on Probability Theory and Statistics Ecole d'Ete de Probabilites de Saint-Flour XXVIII - 1998 /

• Main Authors: Emery, M. (Author, http://id.loc.gov/vocabulary/relators/aut), Nemirovski, A. (http://id.loc.gov/vocabulary/relators/aut), Voiculescu, D. (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Other Authors: Bernard, Pierre (Editor, http://id.loc.gov/vocabulary/relators/edt)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000.
• Edition: 1st ed. 2000.
• Series: Lecture Notes in Mathematics, 1738
• Subjects: Probabilities.; Mathematical analysis.; Analysis (Mathematics).; Differential geometry.; Statistics .; Probability Theory and Stochastic Processes.; Analysis.; Differential Geometry.; Statistical Theory and Methods.

This volume contains lectures given at the Saint-Flour Summer School of Probability Theory during 17th Aug. - 3rd Sept. 1998. The contents of the three courses are the following: - Continuous martingales on differential manifolds. - Topics in non-parametric statistics. - Free probability theory. The...

Table of Contents:

• Variétés, vecteurs, covecteurs, diffuseurs, codiffuseurs
• Semimartingales dans une variété et géométrie d'ordre 2
• Connexions et martingales
• Fonctions convexes et comportement des martingales
• Mouvements browniens et applications harmoniques
• Preface
• Estimating regression functions from Hölder balls
• Estimating regression functions from Sobolev balls
• Spatial adaptive estimation on Sobolev balls
• Estimating signals satisfying differential inequalities
• Aggregation of estimates, I
• Aggregation of estimates, II
• Estimating functionals, I
• Estimating functionals, II
• Noncommutative probability and operator algebra background
• Addition of freely independent noncommutative random variables
• Multiplication of freely independent noncommutative random variables
• Generalized canonical form, noncrossing partitions
• Free independence with amalgamation
• Some basic free processes
• Random matrices in the large N limit
• Free entropy.