# Optimal and Maximin Procedures for Multiple Testing Problems

@article{Rosset2018OptimalAM, title={Optimal and Maximin Procedures for Multiple Testing Problems}, author={S. Rosset and R. Heller and Amichai Painsky and E. Aharoni}, journal={arXiv: Methodology}, year={2018} }

Multiple testing problems are a staple of modern statistical analysis. The fundamental objective of multiple testing procedures is to reject as many false null hypotheses as possible (that is, maximize some notion of power), subject to controlling an overall measure of false discovery, like family-wise error rate (FWER) or false discovery rate (FDR). In this paper we formulate multiple testing of simple hypotheses as an infinite-dimensional optimization problem, seeking the most powerful… Expand

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#### References

SHOWING 1-10 OF 32 REFERENCES

The optimal discovery procedure: a new approach to simultaneous significance testing

- Mathematics
- 2007

The Neyman-Pearson lemma provides a simple procedure for optimally testing a single hypothesis when the null and alternative distributions are known. This result has played a major role in the… Expand

Controlling the false discovery rate: a practical and powerful approach to multiple testing

- Mathematics
- 1995

SUMMARY The common approach to the multiplicity problem calls for controlling the familywise error rate (FWER). This approach, though, has faults, and we point out a few. A different approach to… Expand

The positive false discovery rate: a Bayesian interpretation and the q-value

- Mathematics
- 2003

Multiple hypothesis testing is concerned with controlling the rate of false positives when testing several hypotheses simultaneously. One multiple hypothesis testing error measure is the false… Expand

On the Optimality of Some Multiple Comparison Procedures

- Mathematics
- 1972

Abstract : Optimality criteria formulated in terms of the power functions of the individual tests are given for problems where several hypotheses are tested simultaneously. Subject to the constraint… Expand

Optimal Tests of Treatment Effects for the Overall Population and Two Subpopulations in Randomized Trials, Using Sparse Linear Programming

- Mathematics, Medicine
- Journal of the American Statistical Association
- 2014

This work proposes new, optimal methods for analyzing randomized trials, when it is suspected that treatment effects may differ in two predefined subpopulations, and constructs new multiple testing procedures that satisfy minimax and Bayes optimality criteria. Expand

Adaptive linear step-up procedures that control the false discovery rate

- Mathematics
- 2006

The linear step-up multiple testing procedure controls the false discovery rate at the desired level q for independent and positively dependent test statistics. When all null hypotheses are true, and… Expand

The Emperor’s new tests

- Mathematics
- 1999

In the past two decades, striking examples of allegedly infe- rior likelihood ratio tests (LRT) have appeared in the statistical litera- ture. These examples, which arise in multiparameter hypothesis… Expand

Microarrays, Empirical Bayes and the Two-Groups Model. Rejoinder.

- Computer Science, Mathematics
- 2008

The classic frequentist theory of hypothesis testing developed by Neyman, Pearson, and Fisher has a claim to being the Twentieth Century’s most influential piece of applied mathematics. Something new… Expand

Simultaneous and selective inference: Current successes and future challenges.

- Computer Science, Medicine
- Biometrical journal. Biometrische Zeitschrift
- 2010

The vitality of the field in the future depends upon the ability to continue and address the real needs of statistical analyses in current problems and two application areas offering new challenges have received less attention in the community to date are discussed. Expand

Oracle and Adaptive Compound Decision Rules for False Discovery Rate Control

- Mathematics
- 2007

We develop a compound decision theory framework for multiple-testing problems and derive an oracle rule based on the z values that minimizes the false nondiscovery rate (FNR) subject to a constraint… Expand