A Constant on a Uniform Bound of a Combinatorial Central Limit Theorem

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

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 کامل

A functional combinatorial central limit theorem

The paper establishes a functional version of the Hoeffding combinatorial central limit theorem. First, a pre-limiting Gaussian process approximation is defined, and is shown to be at a distance of the order of the Lyapounov ratio from the original random process. Distance is measured by comparison of expectations of smooth functionals of the processes, and the argument is by way of Stein’s met...

متن کامل

bounds for a combinatorial central limit theorem with involutions

Let E = ((eij))n×n be a fixed array of real numbers such that eij = eji, eii = 0 for 1 ≤ i, j ≤ n. Let the symmetric group be denoted by Sn and the collection of involutions with no fixed points by Πn, that is, Πn = {π ∈ Sn : π 2 = id, π(i) 6= i∀i}. For π uniformly chosen from Πn, let YE = Pn i=1 eiπ(i) and W = (YE − μE)/σE where μE = E(YE) and σ 2 E = Var(YE). Denoting by FW and Φ the distribu...

متن کامل

The Local Limit Theorem: A Historical Perspective

The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...

متن کامل

A Martingale Central Limit Theorem

We present a proof of a martingale central limit theorem (Theorem 2) due to McLeish (1974). Then, an application to Markov chains is given.

متن کامل

ذخیره 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: Journal of Mathematics Research

سال: 2009

ISSN: 1916-9809,1916-9795

DOI: 10.5539/jmr.v1n2p91