Error estimate in the central limit theorem
نویسندگان
چکیده
منابع مشابه
On the error bound in a combinatorial central limit theorem
Let X = {Xij : 1 ≤ i, j ≤ n} be an n× n array of independent random variables where n ≥ 2. Let π be a uniform random permutation of {1,2, . . . , n}, independent of X, and let W =∑ni=1 Xiπ(i). Suppose X is standardized so that EW = 0,Var(W)= 1. We prove that the Kolmogorov distance between the distribution of W and the standard normal distribution is bounded by 451 ∑n i,j=1 E|Xij |3/n. Our appr...
متن کاملCentral Limit Theorem in Multitype Branching Random Walk
A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.
متن کاملThe Martingale Central Limit Theorem
One of the most useful generalizations of the central limit theorem is the martingale central limit theorem of Paul Lévy. Lévy was in part inspired by Lindeberg’s treatment of the central limit theorem for sums of independent – but not necessarily identically distributed – random variables. Lindeberg formulated what, in retrospect, is the right hypothesis, now known as the Lindeberg condition,1...
متن کاملThe Lindeberg central limit theorem
Theorem 1. If μ ∈P(R) has finite kth moment, k ≥ 0, then, writing φ = μ̃: 1. φ ∈ C(R). 2. φ(v) = (i) ∫ R x edμ(x). 3. φ is uniformly continuous. 4. |φ(v)| ≤ ∫ R |x| dμ(x). 1Charalambos D. Aliprantis and Kim C. Border, Infinite Dimensional Analysis: A Hitchhiker’s Guide, third ed., p. 515, Theorem 15.15; http://individual.utoronto.ca/ jordanbell/notes/narrow.pdf 2Onno van Gaans, Probability measu...
متن کاملCentral Limit Theorem Forthe
The Edwards model in one dimension is a transformed path measure for standard Brownian motion discouraging self-intersections. We prove a central limit theorem for the endpoint of the path, extending a law of large numbers proved by Westwater (1984). The scaled variance is characterized in terms of the largest eigenvalue of a one-parameter family of diierential operators, introduced and analyze...
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: Lietuvos matematikos rinkinys
سال: 2008
ISSN: 2335-898X,0132-2818
DOI: 10.15388/lmr.2008.18129