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In this article we propose a general framework for normal approximation using Stein's method.
On the central limit theorem
H. Bergström (1944) · 1944
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A bound for the error in the normal approximation to the distribution of a sum of dependent random variables
C. Stein (1972) · 1971
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Poisson approximation for dependent trials
L. H. Y. Chen (1975) · 1975
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On the normal approximation for sums of mixing random variables
W. Y. Loh (1975) · 1975
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The distribution of leading digits and uniform distribution mod {\rm mod} 1 1
P. Diaconis (1977) · 1977
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Urn models and their application
N. L. Johnson and S. Kotz (1977) · 1977
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An L p L_{p} bound for the remainder in a combinatorial central limit theorem
S. T. Ho and L. H. Y. Chen (1978) · 1978
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Random allocations
V. F. Kolchin, B. A. Sevast ′ · 1978
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A remainder term estimate for the normal approximation in classical occupancy
G. Englund (1981) · 1981
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Exact convergence rates in some martingale central limit theorems
E. Bolthausen (1982) · 1982
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An estimate of the remainder in a combinatorial central limit theorem
E. Bolthausen (1984) · 1984
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Random association of symmetric arrays
A. D. Barbour and G. K. Eagleson (1986) · 1986
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Approximate computation of expectations
C. Stein (1986) · 1986
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Stein’s method and Poisson process convergence
A. D. Barbour (1988) · 1988
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A normal approximation for the number of local maxima of a random function on a graph
P. Baldi, Y. Rinott, and C. Stein (1989) · 1989
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A central limit theorem for decomposable random variables with applications to random graphs
A. D. Barbour, M. Karoński, and A. Ruciński (1989) · 1989
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Closed form summation for classical distributions: variations on a theme of de Moivre
P. Diaconis and S. Zabell (1991) · 1991
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On the rate of convergence in the multivariate CLT
F. Götze (1991) · 1991
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Poisson approximation , volume 2 of Oxford Studies in Probability
A. D. Barbour, L. Holst, and S. Janson (1992) · 1992
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Some examples of normal approximations by Stein’s method
A. Dembo and Y. Rinott (1996) · 1993
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Variational inequalities with examples and an application to the central limit theorem
T. Cacoullos, V. Papathanasiou, and S. A. Utev (1994) · 1994
Cited alongside, same era.
Stein’s method for the gamma distribution and related statistical applications
H. M. Luk (1994) · 1994
Cited alongside, same era.
On the Poisson equation for countable Markov chains: existence of solutions and parameter dependence by probabilistic methods
A. M. Makowski and A. Shwartz (1994) · 1994
Cited alongside, same era.
Stein’s method: some perspectives with applications
L. H. Y. Chen (1998) · 1995
Cited alongside, same era.
The accuracy of the normal approximation to the distribution of the traces of powers of random orthogonal matrices
C. Stein (1995) · 1995
Cited alongside, same era.
Multivariate normal approximations by Stein’s method and size bias couplings
Berry-Esseen bounds for combinatorial central limit theorems and pattern occurrences, using zero and size biasing
L. Goldstein (2005) · 2005
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An explicit Berry-Esseen bound for Student’s t t -statistic via Stein’s method
Q.-M. Shao (2005) · 2005
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Exponential approximation by exchangeable pairs and spectral graph theory
S. Chatterjee, J. Fulman, and A. Röllin (2006) · 2006
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The Berry-Esseen bound for character ratios
Q.-M. Shao and Z.-G. Su (2006) · 2006
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Stein’s method for concentration inequalities
S. Chatterjee (2007) · 2007
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Random graph dynamics
R. Durrett (2007) · 2007
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L. Goldstein and Y. Rinott (1996) · 1996
Cited alongside, same era.
Stein’s method and the zero bias transformation with application to simple random sampling
L. Goldstein and G. Reinert (1997) · 1997
Cited alongside, same era.
Couplings for normal approximations with Stein’s method
G. Reinert (1998) · 1997
Cited alongside, same era.
On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted U U -statistics
Y. Rinott and V. Rotar ′ · 1997
Cited alongside, same era.
Error bound in a central limit theorem of double-indexed permutation statistics
L. Zhao, Z. Bai, C.-C. Chao, and W.-Q. Liang (1997) · 1997
Cited alongside, same era.
Some estimates for the rate of convergence in the CLT for martingales. I
I. Rinott and V. I. Rotar ′ · 1998
Cited alongside, same era.
Normal approximations by Stein’s method
Y. Rinott and V. Rotar ′ · 2000
Cited alongside, same era.
A new method of normal approximation
S. Chatterjee (2008) · 2008
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Local limit theorems for finite and infinite urn models
H.-K. Hwang and S. Janson (2008) · 2008
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Susceptibility in subcritical random graphs
S. Janson and M. J. Luczak (2008) · 2008
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Linear functions on the classical matrix groups
E. Meckes (2008) · 2008
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On L 1 L_{1} bounds for asymptotic normality of some weakly dependent random variables
J. Sunklodas (2008) · 2008
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Univariate approximations in the infinite occupancy scheme
A. D. Barbour (2009) · 2009
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Fluctuations of eigenvalues and second order poincaré inequalities
S. Chatterjee (2009) · 2009
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L p L^{p} bounds for a combinatorial central limit theorem with involutions
S. Ghosh (2009) · 2009
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Stein’s method on wiener chaos
I. Nourdin and G. Peccati (2009) · 2009
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Second order Poincaré inequalities and CLTs on Wiener space
I. Nourdin, G. Peccati, and G. Reinert (2009) · 2009
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Multivariate concentration of measure type results using exchangeable pairs and size biasing
S. Ghosh (2010) · 2010
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A Berry-Esseen bound with applications to counts in the Erdős-Rényi random graph
L. Goldstein (2010) · 2010
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Normal approximation under local dependence
L. H. Y. Chen and Q.-M. Shao (2004) · 2028
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