Glivenko-Cantelli properties of some generalized empirical DF's and strong convergence of generalized L-statistics
نویسندگان
چکیده
منابع مشابه
Empirical Processes: Glivenko–Cantelli Theorems
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 ...
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متن کاملUniform Glivenko–Cantelli Classes
A class of sets, or functions, is said to be P–Glivenko–Cantelli if the empirical measure Pn converges in some sense to the true measure, P , as n → ∞, uniformly over the class of sets or functions. Thus, the notions of Glivenko–Cantelli, and likewise uniform Glivenko–Cantelli are for the most part qualitative assessments of how “well–behaved” a collection of sets or functions is, in the sense ...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 1988
ISSN: 0178-8051,1432-2064
DOI: 10.1007/bf00319105