Empirical Processes: Glivenko–Cantelli Theorems
نویسنده
چکیده
The reader is referred to Chapter 1.6 of Wellner’s Torgnon notes, Chapter ??? of VDVW and Chapter 8.3 of Kosorok. First, a theorem using bracketing entropy. Let (F , ‖ ‖) be a subset of a normed space of real functions f : X → R. Given real functions l and u on X (but not necessarily in F), the bracket [l, u] is defined as the set of all functions f ∈ F satisfying l ≤ f ≤ u. The functions l, u are assumed to have finite norms. An -bracket is a bracket with ‖u − l‖ ≤ . The bracketing number N[] ( ,F ‖ ‖) is the minimum number of -brackets with which F can be covered and the bracketing entropy is the log of this number.
منابع مشابه
Donsker and Glivenko-Cantelli theorems for a class of processes generalizing the empirical process
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