Gaussian approximations for high-dimensional non-degenerate U-statistics via exchangeable pairs

2021 ◽  
pp. 109295
Author(s):  
Guanghui Cheng ◽  
Zhi Liu ◽  
Liuhua Peng
Keyword(s):  
High Dimensional ◽  
U Statistics ◽  
Exchangeable Pairs

scholarly journals Random subgraph counts and U-statistics: multivariate normal approximation via exchangeable pairs and embedding

2010 ◽  
Vol 47 (2) ◽  
pp. 378-393 ◽  
Author(s):  
Gesine Reinert ◽  
Adrian Röllin
Keyword(s):  
Dimensional Space ◽  
Multivariate Normal ◽  
New Approach ◽  
U Statistics ◽  
Normal Approximations ◽  
Random Subgraph ◽  
Exchangeable Pairs ◽  
Higher Dimensional ◽  
Multivariate Normal Approximation ◽  
Linearity Condition

In Reinert and Röllin (2009) a new approach - called the ‘embedding method’ - was introduced, which allows us to make use of exchangeable pairs for normal and multivariate normal approximations with Stein's method in cases where the corresponding couplings do not satisfy a certain linearity condition. The key idea is to embed the problem into a higher-dimensional space in such a way that the linearity condition is then satisfied. Here we apply the embedding to U-statistics as well as to subgraph counts in random graphs.

scholarly journals Asymptotically independent U-statistics in high-dimensional testing

2021 ◽  
Vol 49 (1) ◽  
pp. 154-181 ◽  
Author(s):  
Yinqiu He ◽  
Gongjun Xu ◽  
Chong Wu ◽  
Wei Pan
Keyword(s):  
High Dimensional ◽  
U Statistics

scholarly journals Random subgraph counts and U-statistics: multivariate normal approximation via exchangeable pairs and embedding

2010 ◽  
Vol 47 (02) ◽  
pp. 378-393
Author(s):  
Gesine Reinert ◽  
Adrian Röllin
Keyword(s):  
Dimensional Space ◽  
Multivariate Normal ◽  
New Approach ◽  
U Statistics ◽  
Normal Approximations ◽  
Random Subgraph ◽  
Exchangeable Pairs ◽  
Higher Dimensional ◽  
Multivariate Normal Approximation ◽  
Linearity Condition

In Reinert and Röllin (2009) a new approach - called the ‘embedding method’ - was introduced, which allows us to make use of exchangeable pairs for normal and multivariate normal approximations with Stein's method in cases where the corresponding couplings do not satisfy a certain linearity condition. The key idea is to embed the problem into a higher-dimensional space in such a way that the linearity condition is then satisfied. Here we apply the embedding to U-statistics as well as to subgraph counts in random graphs.

scholarly journals Approximating high-dimensional infinite-order $U$-statistics: Statistical and computational guarantees

2019 ◽  
Vol 13 (2) ◽  
pp. 4794-4848
Author(s):  
Yanglei Song ◽  
Xiaohui Chen ◽  
Kengo Kato
Keyword(s):  
Infinite Order ◽  
High Dimensional ◽  
U Statistics

High-Dimensional Probability

2018 ◽  
Author(s):  
Roman Vershynin
Keyword(s):  
High Dimensional

The Semantic Credentials of High-Dimensional Memory Models

2014 ◽  
Author(s):  
Curt Burgess ◽  
Sarah Maples
Keyword(s):  
Memory Models ◽  
High Dimensional
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