Open Access
2014 Berry-Esseen bounds for estimating undirected graphs
Larry Wasserman, Mladen Kolar, Alessandro Rinaldo
Electron. J. Statist. 8(1): 1188-1224 (2014). DOI: 10.1214/14-EJS928


We consider the problem of providing nonparametric confidence guarantees — with finite sample Berry-Esseen bounds — for undirected graphs under weak assumptions. We do not assume sparsity or incoherence. We allow the dimension $D$ to increase with the sample size $n$. First, we prove lower bounds that show that if we want accurate inferences with weak assumptions then $D$ must be less than $n$. In that case, we show that methods based on Normal approximations and on the bootstrap lead to valid inferences and we provide new Berry-Esseen bounds on the accuracy of the Normal approximation and the bootstrap. When the dimension is large relative to sample size, accurate inferences for graphs under weak assumptions are not possible. Instead we propose to estimate something less demanding than the entire partial correlation graph. In particular, we consider: cluster graphs, restricted partial correlation graphs and correlation graphs.


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Larry Wasserman. Mladen Kolar. Alessandro Rinaldo. "Berry-Esseen bounds for estimating undirected graphs." Electron. J. Statist. 8 (1) 1188 - 1224, 2014.


Published: 2014
First available in Project Euclid: 12 August 2014

zbMATH: 1298.62089
MathSciNet: MR3263117
Digital Object Identifier: 10.1214/14-EJS928

Primary: 62H12
Secondary: 62H10

Keywords: graphical models , High dimensional inference

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.8 • No. 1 • 2014
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