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https://doi.org/10.1214/11-AIHP473
Title: | Stein's method in high dimensions with applications | Authors: | Röllin, A. | Keywords: | Curie-Weiss model Gaussian interpolation Last passage percolation on thin rectangles Sherrington-Kirkpatrick model Stein's method |
Issue Date: | May-2013 | Citation: | Röllin, A. (2013-05). Stein's method in high dimensions with applications. Annales de l'institut Henri Poincare (B) Probability and Statistics 49 (2) : 529-549. ScholarBank@NUS Repository. https://doi.org/10.1214/11-AIHP473 | Abstract: | Let h be a three times partially differentiable function on Rn, let X = (X1, +⋯, Xn) be a collection of real-valued random variables and let Z = (Z1, +⋯, Zn) be a multivariate Gaussian vector. In this article, we develop Stein's method to give error bounds on the difference Eh(X) - Eh(Z) in cases where the coordinates of X are not necessarily independent, focusing on the high dimensional case n→∞. In order to express the dependency structure we use Stein couplings, which allows for a broad range of applications, such as classic occupancy, local dependence, Curie-Weiss model, etc. We will also give applications to the Sherrington-Kirkpatrick model and last passage percolation on thin rectangles. © 2013 Association des Publications de l'Institut Henri Poincaré. | Source Title: | Annales de l'institut Henri Poincare (B) Probability and Statistics | URI: | http://scholarbank.nus.edu.sg/handle/10635/105396 | ISSN: | 02460203 | DOI: | 10.1214/11-AIHP473 |
Appears in Collections: | Staff Publications |
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