Randomised P-values and nonparametric procedures in multiple testing

References

• Benjamini , Y. and Hochberg , Y. 1995 . Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing . Journal of the Royal Statistical Society Series B , 57 : 289 – 300 .
   Web of Science ®Google Scholar
• Benjamini , Y. and Yekutieli , D. 2001 . The Control of the False Discovery Rate in Multiple Testing Under Dependency . The Annals of Statistics , 29 : 1165 – 1188 .
   Web of Science ®Google Scholar
• Berger , R. L. and Casella , G. 2005 . Comment: Fuzzy and Randomized Confidence Intervals and P-Values . Statistical Science , 20 : 372 – 374 .
   Web of Science ®Google Scholar
• Bonferroni , C. 1936 . Teoria statistica delle classi e calcolo delle probabilità . Pubblicazioni del R Istituto Superiore di Scienze Economiche e Commerciali di Firenze , 8 : 3 – 62 .
   Google Scholar
• Cox , D. R. and Hinkley , D. V. 1974 . Theoretical Statistics , London : Chapman and Hall .
   Google Scholar
• Dudoit , S. and van der Laan , M. J. 2008 . Multiple Testing Procedures with Applications to Genomics , New York : Springer . Springer Series in Statistics
   Google Scholar
• Efron , B. 2004 . Large-Scale Simultaneous Hypothesis Testing: The Choice of a Null Hypothesis . Journal of the American Statistical Association , 99 : 96 – 104 .
   Web of Science ®Google Scholar
• Efron , B. 2007 . Size, Power and False Discovery Rates . The Annals of Statistics , 35 : 1351 – 1377 .
   Web of Science ®Google Scholar
• Efron , B. 2008 . Microarrays, Empirical Bayes and the Two-Group Model . Statistical Science , 23 : 1 – 22 .
   Web of Science ®Google Scholar
• Efron , B. , Tibshirani , R. , Storey , J. D. and Tusher , P. 2001 . Empirical Bayes Analysis of a Microarray Experiment . Journal of the American Statistical Association , 96 : 1151 – 1160 .
   Web of Science ®Google Scholar
• Efron , B. , Turnbull , B. and Narasimhan , B. 2009 . Locfdr: Computes Local False Discovery Rates . R Package Version 1.1-6, CRAN. http://cran.r-project.org/web/packages/locfdr/.
   Google Scholar
• Genovese , C. and Wasserman , L. 2004 . A Stochastic Process Approach to False Discovery Rate Control . Annals of Statistics , 32 : 1035 – 1061 .
   Web of Science ®Google Scholar
• Geyer , C. J. and Meeden , G. D. 2005 . Fuzzy and Randomized Confidence Intervals and P-Values’ (with comments and a rejoinder by the authors) . Statistical Science , 20 : 358 – 387 .
   Web of Science ®Google Scholar
• Gilbert , P. B. 2005 . A Modified False Discovery Rate Multiple-Comparisons Procedure for Discrete Data, Applied to Human Immunodeficiency Virus Genetics . Journal of the Royal Statistical Society Series C , 54 : 143 – 158 .
   Web of Science ®Google Scholar
• Gutman , R. and Hochberg , Y. 2007 . Improved Multiple Test Procedures for Discrete Distributions: New Ideas and Analytical Review . Journal of Statistical Planning and Inference , 137 : 2380 – 2393 .
   Web of Science ®Google Scholar
• Hommel , G. and Krummenauer , F. 1998 . Improvements and Modifications of Tarone's Multiple Test Procedure for Discrete Data . Biometrics , 54 : 673 – 681 .
   Web of Science ®Google Scholar
• Jin , J. and Cai , T. T. 2007 . Estimating the Null and the Proportion of Nonnull Effects in Large-Scale Multiple Comparisons . Journal of the American Statistical Association , 102 : 495 – 506 .
   Web of Science ®Google Scholar
• Korn , E. L. , Troendle , J. F. , McShane , L. M. and Simon , R. 2004 . Controlling the Number of False Discoveries: Application to High-Dimensional Genomic Data . Journal of Statistical Planning and Inference , 124 : 379 – 398 .
   Web of Science ®Google Scholar
• Kulinskaya , E. and Lewin , A. 2009 . On Fuzzy Familywise Error Rate and False Discovery Rate Procedures for Discrete Distributions . Biometrika , 96 : 201 – 211 .
   Web of Science ®Google Scholar
• Lancaster , H. O. 1961 . Significance Tests in Discrete Distributions . Journal of the American Statistical Association , 56 : 223 – 234 .
   Web of Science ®Google Scholar
• Neyman , J. and Pearson , E. 1933 . On the Problem of the Most Efficient Tests of Statistical Hypotheses . Philosophical Transactions of the Royal Society of London. Series A , 231 : 289 – 337 .
   Google Scholar
• Pollard , K. S. and van der Laan , M. J. 2004 . Choice of a Null Distribution in Resampling-Based Multiple Testing . Journal of Statistical Planning and Inference , 125 : 85 – 100 .
   Web of Science ®Google Scholar
• Randles , R. H. and Wolfe , D. A. 1979 . Introduction to the Theory of Nonparametric Statistics , New York–Chichester–Brisbane : John Wiley & Sons . Wiley Series in Probability and Mathematical Statistics
   Google Scholar
• Roth , A. J. 1999 . Multiple Comparison Procedures for Discrete Test Statistics . Journal of Statistical Planning and Inference , 82 : 101 – 117 . (Multiple Comparisons; Tel Aviv, 1996)
   Web of Science ®Google Scholar
• Ruppert , D. , Nettleton , D. and Hwang , J. T. 2007 . Exploring the Information in p-Values for the Analysis and Planning of Multiple-Test Experiments . Biometrics , 63 : 483 – 495 .
   PubMed Web of Science ®Google Scholar
• Sarkar , S. K. 2002 . Some Results on False Discovery Rate in Stepwise Multiple Testing Procedures . The Annals of Statistics , 30 : 239 – 257 .
   Web of Science ®Google Scholar
• Storey , J. 2002 . A Direct Approach to False Discovery Rates . Journal of the Royal Statistical Society. Series B , 64 : 479 – 498 .
   Google Scholar
• Storey , J. 2003 . The Positive False Discovery Rate: A Bayesian Interpretation and the q-Value . The Annals of Statistics , 31 : 2012 – 2035 .
   Web of Science ®Google Scholar
• Sun , W. and Cai , T. T. 2007 . Oracle and Adaptive Compound Decision Rules for False Discovery Rate Control . Journal of the American Statistical Association , 102 : 901 – 912 .
   Web of Science ®Google Scholar
• Tarone , R. E. 1990 . A Modified Bonferroni Method for Discrete Data . Biometrics , 46 : 515 – 522 .
   PubMed Web of Science ®Google Scholar
• Timmons , J. , Wennmalm , K. , Larsson , O. , Walden , T. , Lassmann , T. , Petrovic , N. , Hamilton , D. , Gimeno , R. , Wahlestedt , C. , Baar , K. , Nedergaard , J. and Cannon , B. Myogenic Gene Expression Signature Establishes that Brown and White Adipocytes Originate from Distinct Cell Lineages . Proceedings of the National Academy of Sciences of the United States of America . Vol. 104(11) , pp. 4401 – 4406 .
   Google Scholar
• van der Laan , M. J. and Hubbard , A. E. 2006 . Quantile-Function Based Null Distribution in Resampling Based Multiple Testing . Statistical Applications in Genetics and Molecular Biology , 5 (electronic) Art. 14, 30pp
   Web of Science ®Google Scholar
• Westfall , P. H. and Soper , K. A. 1998 . Weighted Multiplicity Adjustments for Animal Carcinogenicity Tests . Journal of Biopharmaceutical Statitics , 8 : 23 – 44 .
   PubMedGoogle Scholar
• Westfall , P. H. and Soper , K. A. 2001 . Using Priors to Improve Multiple Animal Carcinogenicity Tests . Journal of the American Statistical Association , 96 : 827 – 834 .
   Web of Science ®Google Scholar
• Westfall , P. H. and Troendle , J. H. 2008 . Multiple Testing with Minimal Assumptions . Biometrical Journal , 50 : 745 – 755 .
   PubMed Web of Science ®Google Scholar
• Westfall , P. H. and Wolfinger , R. D. 1997 . Multiple Tests with Discrete Distributions . The American Statistician , 51 : 3 – 8 .
   Web of Science ®Google Scholar
• Westfall , P. H. and Young , S. S. 1989 . p Value Adjustments for Multiple Tests in Multivariate Binomial Models . Journal of the American Statistical Association , 84 : 780 – 786 .
   Web of Science ®Google Scholar
• Yekutieli , D. and Benjamini , Y. 1999 . Resampling-Based False Discovery Rate Controlling Multiple Test Procedures for Correlated Test Statistics . Journal of Statistical Planning and Inference , 82 : 171 – 196 .
   Web of Science ®Google Scholar