Donsker Classes and Random Geometry
Talagrand, Michel
Ann. Probab., Tome 15 (1987) no. 4, p. 1327-1338 / Harvested from Project Euclid
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Let $\mathscr{F}$ be a class of square integrable functions. We give necessary and sufficient random geometric conditions for the empirical process indexed by $\mathscr{F}$ to satisfy the CLT. These conditions roughly mean that the trace of $\mathscr{F}$ on a random sample is a small (for the $l^1$ norm) perturbation of a set which is nice for the $l^2$ norm.
Publié le : 1987-10-14
Classification:  Central limit theorems,  empirical processes,  functional Donsker classes,  metric entropy,  60F17,  60B12,  60F05,  62E20 
@article{1176991979,
     author = {Talagrand, Michel},
     title = {Donsker Classes and Random Geometry},
     journal = {Ann. Probab.},
     volume = {15},
     number = {4},
     year = {1987},
     pages = { 1327-1338},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176991979}
}

Talagrand, Michel. Donsker Classes and Random Geometry. Ann. Probab., Tome 15 (1987) no. 4, pp.  1327-1338. http://gdmltest.u-ga.fr/item/1176991979/