Some probability inequalities for ordered MTP\(_2\) random variables: a proof of the Simes conjecture

DOI10.1214/aos/1028144846zbMath0929.62065OpenAlexW2060072410WikidataQ123011083 ScholiaQ123011083MaRDI QIDQ1807084

Publication date: 9 November 1999

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1028144846

zbMATH Keywords

positive dependence P-values multivariate totally positive of order 2 Simes test

Mathematics Subject Classification ID

Multivariate analysis (62H99) Inequalities; stochastic orderings (60E15) Hypothesis testing in multivariate analysis (62H15)

Related Items

Admissible ways of merging \(p\)-values under arbitrary dependence, Simultaneous Statistical Inference in Dynamic Factor Models, Performance of unit root tests in unbalanced panels: experimental evidence, Development of gatekeeping strategies in confirmatory clinical trials, Nonstationary-volatility robust panel unit root tests and the great moderation, FDR-controlling stepwise procedures and their false negatives rates, Union-intersection principle and constrained statistical inference, Testing the equality of multivariate means when \(p>n\) by combining the Hotelling and Simes tests, On the Simes inequality in elliptical models, An Intersection Test for Panel Unit Roots, On generalized Simes critical constants, Intersection tests for the cointegrating rank in dependent panel data, Bivariate high-level exceedance and the Chen-Stein theorem in genomics multiple hypothesis testing perspectives, On Samuel's \(p\)-value model and the Simes test under dependence, On the Simes test under dependence, The sequential rejection principle of familywise error control, Trade-off Between Validity and Efficiency of Merging P-Values Under Arbitrary Dependence, Filtering the Rejection Set While Preserving False Discovery Rate Control, Testing partial conjunction hypotheses under dependency, with applications to meta-analysis, Step-up and step-down methods for testing multiple hypotheses in sequential experiments, On a class of prior distributions that accounts for uncertainty in the data, Sequential tests of multiple hypotheses controlling false discovery and nondiscovery rates, Power-enhanced multiple decision functions controlling family-wise error and false discovery rates, Testing with \(\mathrm{p}^*\)-values: between p-values, mid p-values, and e-values, A multivariate test against spurious long memory, On stepwise control of the generalized familywise error rate, A comprehensive error rate for multiple testing, Deriving and comparing the distribution for the number of false positives in single step methods to control \(k\)-FWER, On adaptive procedures controlling the familywise error rate, Strong approximations of level exceedences related to multiple hypothesis testing, α-Investing: a Procedure for Sequential Control of Expected False Discoveries, A comparative simulation of multiple testing procedures in circular data problems, FDR- and FWE-controlling methods using data-driven weights, Discovering the False Discovery Rate, Screening for Partial Conjunction Hypotheses, Modified Simes' critical values under independence, A look at multiplicity through misclassification, Nonparametric multiple comparison procedures for unbalanced two-way layouts, Negative dependence and the Simes inequality, Stepup procedures controlling generalized FWER and generalized FDR, Two-stage stepup procedures controlling FDR, False discovery rate control for non-positively regression dependent test statistics, Generalizing Simes' test and Hochberg's stepup procedure, A nonparametric coherent confidence procedure, False discovery and false nondiscovery rates in single-step multiple testing procedures, Familywise Robustness Criteria for Multiple-Comparison Procedures, A review of modern multiple hypothesis testing, with particular attention to the false discovery proportion, Asymptotic sharpness of product-type inequalities for maxima of random variables with applications in multiple comparisons, A flexible choice of critical constants for the improved hybrid Hochberg-Hommel procedure, Optimally weighted, fixed sequence and gatekeeper multiple testing procedures, Modified Simes' critical values under positive dependence, Further results on controlling the false discovery proportion, Multiple testing for exploratory research, Robustness of multiple testing procedures against dependence, On the Exact Size of Tests of Treatment Effects in Multi-Arm Clinical Trials, On a new class of multivariate prior distributions: theory and application in reliability, Some remarks on Simes-type multiple tests of significance., Nonparametric multiple comparison procedures for unbalanced one-way factorial designs, Group sequential BH and its adaptive versions controlling the FDR, Positive Dependence and Weak Convergence, A note on the monotonicity of the critical values of a step-up test, Generalizations of the familywise error rate, The control of the false discovery rate in multiple testing under dependency., Some results on false discovery rate in stepwise multiple testing procedures., An appraisal of some aspects of statistical inference under inequality constraints

Cites Work