A Multivariate CLT for Decomposable Random Vectors with Finite Second Moments

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Multivariate normal approximation with Stein’s method of exchangeable pairs under a general linearity condition (2007, result): “This reflects the fact that we make use of Lemma 2.6, which is motivated by Goldstein and Rinott (1996), whereas Chatterjee and Meckes (2008) prove new bounds on the solutions of (2.4), but only for Σ = Id; see also Raič (2004) for similar results.”
A NEW METHOD OF NORMAL APPROXIMATION (2006, unknown): “For a different proof of the bound on ‖φ‖∞, see Lemma 1 in [33].”
On Stein's method for multivariate normal approximation (2009, methodology): “This general definition of Mk is a departure from what was done by Raič in [15]; there, smoothness conditions on functions are also given in coordinate-independent ways, and M1 and M2 are defined as they are here, but in case k = 3, the quantity M3 is defined as the Lipschitz constant of the Hessia”
Stein couplings for normal approximation (2010, methodology): “(6.6) {83} (see Stein (1972) and Raič (2004)).”
MULTIVARIATE NORMAL APPROXIMATION USING EXCHANGEABLE PAIRS (2007, unknown): “Introduction Stein’s method was introduced by Charles Stein (1972) as a tool for proving central limit theorems for sums of dependent random variables.”