A multivariate Berry–Esseen theorem with explicit constants

By Martin Raivc. Bernoulli, 2018

104 citations recorded by the source corpus.

We provide a Lyapunov type bound in the multivariate central limit theorem for sums of independent, but not necessarily identically distributed random vectors. The error in the normal approximation is estimated for certain classes of sets, which include the class of measurable convex sets. The error bound is stated with explicit constants. The result is proved by means of Stein’s method. In addition, we improve the constant in the bound of the Gaussian perimeter of convex sets.

Subfields: Geometry and Topology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/598592cf94c97820de8257899e1913ced6b4d6bf

How researchers see this paper

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In Geometry and Topology

1. Yuta Koike
2. G. Alastair Young
3. Daniel Garcia Rasines
4. Xiao Fang

In Statistics and Probability

1. Yuta Koike
2. G. Alastair Young
3. Daniel Garcia Rasines
4. Xiao Fang
5. Victor Chernozhukov
6. John C. Duchi
7. D. Chetverikov
8. Cms Collaboration

Citations in the corpus

• High-dimensional central limit theorems by Stein’s method (2020, background): “See Raič (2019) for a bound with explicit constant.”
• Splitting strategies for post-selection inference (2021, methodology): “The good performance of this estimator in sparse models was demonstrated in Reid et al. (2016). Many other methods are available; e.g. Fan et al. (2012) and Bayati et al.”