A Glivenko-Cantelli theorem for empirical measures of independent but non-identically distributed random variables
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 ...
متن کاملComparison of Sums of Independent Identically Distributed Random Variables
Let Sk be the k-th partial sum of Banach space valued independent identically distributed random variables. In this paper, we compare the tail distribution of ‖Sk‖ with that of ‖Sj‖, and deduce some tail distribution maximal inequalities. The main result of this paper was inspired by the inequality from [dP–M] that says that Pr(‖X1‖ > t) ≤ 5 Pr(‖X1 +X2‖ > t/2) whenever X1 and X2 are independent...
متن کاملGenerating the Maximum of Independent Identically Distributed Random Variables
Frequently the need arises for the computer generation of variates that are exact/y distributed as 2 = max(X,, . , X.) where X,, . . . , X, form a sequence of independent identically distributed random variables. For large n the individual generation of the Xi’s is unfeasible, and the inversion-of-a-beta-variate is potentially inaccurate. In this paper, we discuss and compare the corrected inve...
متن کاملThe Glivenko Cantelli Theorem and its Generalizations
In this note we will study upper bounds of random variables of the type sup A∈A |ν n (A) − ν(A)| , where A is a class of sets that needs to fulll certain assumptions. These bounds are important tools in the analysis of learning processes and probabilistic theories of pattern recognition. The presentation given here is based on [DGL96].
متن کاملSaddlepoint approximations for the sum of independent non-identically distributed binomial random variables
We discuss saddlepoint approximations to the distribution of the sum of independent nonidentically distributed binomial random variables. The saddlepoint solution is the root of a polynomial equation. The paper provides an expression for the coefficients of a polynomial of any degree, the root of which can be found using a simple root-finding algorithm. We examine the accuracy of the saddlepoin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 1981
ISSN: 0304-4149
DOI: 10.1016/0304-4149(81)90033-8