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Non-uniform bounds for geometric approximation
Statistics & Probability Letters, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Phillips, M. J., Weinberg, Graham V.
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A non-uniform Berry-Esseen bound via Stein's method
Probability Theory and Related Fields, 2001Let \(X_1,X_2,\ldots,X_n\) be independent random variables with zero means and suppose \(W=\sum_{i=1}^nX_i\) has unit variance. The main result (Theorem~2.2) is that there exists an absolute constant \(C\) such that for all real numbers \(x\), \[ |F(x)-\Phi(x)|\leq C\sum_{i=1}^n\left\{\frac{E X_i^2I(|X_i|>1+|x|)}{(1+|x|)^2} +\frac{E|X_i|^3I(|X_i|\leq 1+
Chen, L.H.Y., Shao, Q.-M.
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Non-uniform hyperbolicity and universal bounds for S-unimodal maps
Inventiones Mathematicae, 1998An \(S\)-unimodal map \(f\) is said to satisfy the Collet-Eckmann condition if the lower Lyapunov exponent at the critical value is positive. If the infimum of the Lyapunov exponent over all periodic points is positive then \(f\) is said to have a uniform hyperbolic structure.
Nowicki, Tomasz, Sands, Duncan
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Performance bounds of non-uniform signaling over AWGN channels
1999 IEEE Communications Theory Mini-Conference (Cat. No.99EX352), 1999We present two bounds (one lower bound and one upper bound) on the probability of a union of a finite number of events. The bounds-which are expressed in terms of only the individual event probabilities and the pairwise event probabilities-are applied to examine the symbol error (P/sub s/) and bit error (P/sub b/) probabilities of an uncoded ...
H. Kuai, F. Alajagi, G. Takahara
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Non uniform bound on a combinatorial central limit theorem
Communications in Statistics - Theory and Methods, 2015ABSTRACTIn this paper, we give a non uniform bound on combinatorial central limit theorem by using Stein’s method. This improves the result of Neammanee and Rattanawong (2009) from the finiteness of the sixth moment to the finiteness of the third moment.
W. Simcharoen, K. Neammanee
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Non-uniform Bounds for Independent Random Variables
2011Continuing the consideration of the independent case, Chap. 8 presents non-uniform bounds for sums of independent random variables. In particular, by use of non-uniform concentration inequalities and the Bennett–Hoeffding inequality, bounds for the absolute difference between the distribution function F(z) of a sum of independent variables and the ...
Louis H. Y. Chen +2 more
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Uniform and Non-uniform Bounds Under Local Dependence
2011Chapter 9 considers local dependence using the K-function approach, and obtains both uniform and non-uniform Berry–Esseen bounds. The results are applied to certain scan statistics, and yield a general theorem when the local dependence can be expressed in terms of a dependency graph whose vertices are the underlying variables, and where two non ...
Louis H. Y. Chen +2 more
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Non-uniform Berry-Esseen Bounds for Coordinate Symmetric Random Vectors with Applications
Acta Mathematica Vietnamica, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Le Van Thanh, Nguyen Ngoc Tu
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Uniform and Non-uniform Bounds for Non-linear Statistics
2011Chapter 10 develops uniform and non-uniform bounds for non-linear functions T(X 1,…,X n ), of independent random variables X 1,…,X n , that can be well approximated by a linear term plus a non-linear remainder. Applications include U-statistics, L-statistics and random sums.
Louis H. Y. Chen +2 more
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