# Asymptotic control of FWER under Gaussian assumption: application to correlation tests

@article{Achard2020AsymptoticCO, title={Asymptotic control of FWER under Gaussian assumption: application to correlation tests}, author={Sophie Achard and Pierre Borgnat and Ir{\`e}ne Gannaz}, journal={arXiv: Statistics Theory}, year={2020} }

In many applications, hypothesis testing is based on an asymptotic distribution of statistics. The aim of this paper is to clarify and extend multiple correction procedures when the statistics are asymptotically Gaussian. We propose a unified framework to prove their asymptotic behavior which is valid in the case of highly correlated tests. We focus on correlation tests where several test statistics are proposed. All these multiple testing procedures on correlations are shown to control FWER…

## One Citation

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## References

SHOWING 1-10 OF 62 REFERENCES

### Large-Scale Multiple Testing of Correlations

- MathematicsJournal of the American Statistical Association
- 2016

This article considers large-scale simultaneous testing for correlations in both the one-sample and two-sample settings and shows that the proposed procedures asymptotically control the overall false discovery rate and false discovery proportion at the nominal level.

### Graph inference by multiple testing with application to Neuroimaging

- Mathematics, Computer Science
- 2018

This thesis investigates the problem of the inference of the structure of an undirected graphical model by a multiple testing procedure, and presents some multiple testing procedures, well-suited for correlation tests, which provide an asymptotic control of the FWER.

### Control of the false discovery rate under dependence using the bootstrap and subsampling

- Mathematics, Economics
- 2008

This paper considers the problem of testing s null hypotheses simultaneously while controlling the false discovery rate (FDR). Benjamini and Hochberg (J. R. Stat. Soc. Ser. B 57(1):289–300, 1995)…

### Wavelet-based graph inference using multiple testing

- Computer ScienceOptical Engineering + Applications
- 2019

This paper describes a whole procedure which estimates the graph from multivariate time series, and proves theoretically that the Family Wise Error Rate (FWER) is asymptotically controlled for any graph structures.

### Regularized estimation of large-scale gene association networks using graphical Gaussian models

- Computer ScienceBMC Bioinformatics
- 2009

A general framework for combining regularized regression methods with the estimation of Graphical Gaussian models is investigated, which includes various existing methods as well as two new approaches based on ridge regression and adaptive lasso, respectively.

### Brain networks of rats under anesthesia using resting-state fMRI: comparison with dead rats, random noise and generative models of networks

- BiologyJournal of neural engineering
- 2020

Evaluating the robustness of brain network estimations, discriminate them under anesthesia and compare them to generative models indicates that the use of correlations in the context of fMRI signals is robust but must be treated with caution.

### Exact and Approximate Stepdown Methods for Multiple Hypothesis Testing

- Mathematics
- 2003

Consider the problem of testing k hypotheses simultaneously. In this article we discuss finite- and large-sample theory of stepdown methods that provide control of the familywise error rate (FWE). To…

### Nonlinear Shrinkage Estimation of Large-Dimensional Covariance Matrices

- Mathematics
- 2011

Many statistical applications require an estimate of a covariance matrix and/or its inverse. When the matrix dimension is large compared to the sample size, which happens frequently, the sample…

### Sparse permutation invariant covariance estimation

- Computer Science, Mathematics
- 2008

A method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings using a penalized normal likelihood approach and forces sparsity by using a lasso-type penalty is proposed.