Corpus ID: 88524095

Optimal and Maximin Procedures for Multiple Testing Problems

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

Figures and Tables from this paper

Optimal FDR control in the two-group model
The highly influential two group model in testing a large number of statistical hypothesis assumes that the test statistics come from a mixture of a high probability null distribution and a lowExpand
Optimal control of false discovery criteria in the two‐group model
This paper addresses the challenge of controlling optimally the popular false discovery rate (fDR) or positive FDR (pFDR) rather than mFDR in the two group model and suggests that the pFDR is (arguably) the preferred error measure to control optimally for theTwo group model. Expand
Only closed testing procedures are admissible for controlling false discovery proportions
We consider the class of all multiple testing methods controlling tail probabilities of the false discovery proportion, either for one random set or simultaneously for many such sets. This classExpand
False discovery rate control with unknown null distribution: is it possible to mimic the oracle?
Classical multiple testing theory prescribes the null distribution, which is often a too stringent assumption for nowadays large scale experiments. This paper presents theoretical foundations toExpand
A model and test for coordinated polygenic epistasis in complex traits
This work develops a model for structured polygenic epistasis, called coordinated epistasis (CE), and proves that several recent theories of genetic architecture fall under the formal umbrella of CE, and proposes the even-odd (EO) test and proves it is calibrated in a range of realistic biological models. Expand
Coordinated Interaction: A model and test for globally signed epistasis in complex traits
A model for structured polygenic epistasis, called Coordinated Interaction (CI), is developed and it is proved that several recent theories of genetic architecture fall under the formal umbrella of CI, a new dimension of Genetic architecture that can capture structured, systemic interactions in complex human traits. Expand


The optimal discovery procedure: a new approach to simultaneous significance testing
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 theExpand
Controlling the false discovery rate: a practical and powerful approach to multiple testing
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 toExpand
The positive false discovery rate: a Bayesian interpretation and the q-value
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 falseExpand
On the Optimality of Some Multiple Comparison Procedures
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 constraintExpand
Optimal Tests of Treatment Effects for the Overall Population and Two Subpopulations in Randomized Trials, Using Sparse Linear Programming
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
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, andExpand
The Emperor’s new tests
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 hypothesisExpand
Microarrays, Empirical Bayes and the Two-Groups Model. Rejoinder.
  • B. Efron
  • 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 newExpand
Simultaneous and selective inference: Current successes and future challenges.
  • Y. Benjamini
  • 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
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 constraintExpand