A course on empirical processes. (English) Zbl 0554.60029

Dudley, R. M.

Ecole d’été de probabilités de Saint-Flour XII - 1982, Lect. Notes Math. 1097, 1-142 (1984).

[For the entire collection see Zbl 0541.00006.]
This booklet deals with large sample theory of empirical processes indexed by quite arbitrary parameter sets. Special emphasis is given to almost sure uniform convergence (with rates) and functional central limit theorems. This is done within the framework of the so-called Vapnik- Cervonenkis setup. The author also exploits the measure theoretic aspects arising in the absence of separability. Some of the work is strongly related to the recent books by P. Gaenssler, Empirical Processes, IMS Lect. Notes Ser. and D. Pollard, Convergence of stochastic processes, Springer (1984).

Reviewer: W.Stute

MSC:

60Fxx	Limit theorems in probability theory
60G15	Gaussian processes
60E15	Inequalities; stochastic orderings

Keywords:

Glivenko-Cantelli convergence; Donsker classes; uniform convergence; functional central limit theorems; Vapnik-Cervonenkis setup