Publication Cover
Sequential Analysis
Design Methods and Applications
Volume 31, 2012 - Issue 2
328
Views
21
CrossRef citations to date
0
Altmetric
Original Articles

Sequential Bonferroni Methods for Multiple Hypothesis Testing with Strong Control of Family-Wise Error Rates I and II

&
Pages 238-262 | Received 28 Dec 2011, Accepted 06 Feb 2012, Published online: 10 Apr 2012

REFERENCES

  • Armitage , P. ( 1950 ). Sequential Analysis with More Than Two Alternative Hypotheses, and Its Relation to Discriminant Function Analysis , Journal of Royal Statistical Society, Series B 12 : 137 – 144 .
  • Baillie , D. H. ( 1987 ). Multivariate Acceptance Sampling—Some Applications to Defence Procurement , Statistician 36 : 465 – 478 .
  • Bartroff , J. and Lai , T. L. ( 2010 ). Multistage Tests of Multiple Hypotheses , Communications in Statistics—Theory and Methods 39 : 1597 – 1607 .
  • Baum , C. W. and Veeravalli , V. V. ( 1994 ). A Sequential Procedure for Multihypotheses Testing , IEEE Transactions on Information Theory 40 : 1994 – 2007 .
  • Benjamini , Y. , Bertz , F. , and Sarkar , S. ( 2004 ). Recent Developments in Multiple Comparison Procedures, IMS Lecture Notes – Monograph Series , Beachwood : Institute of Mathematical Statistics .
  • Benjamini , Y. and Hochberg , Y. ( 1995 ). Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing , Journal of Royal Statistical Society, Series B 57 : 289 – 300 .
  • Berger , J. O. ( 1985 ). Statistical Decision Theory , New York : Springer .
  • Betensky , R. A. ( 1996 ). An O'Brien-Fleming Sequential Trial for Comparing Three Treatments , Annals of Statistics 24 : 1765 – 1791 .
  • Billingsley , P. ( 1995 ). Probability and Measure , New York : Wiley .
  • Borovkov , A. A. ( 1997 ). Matematicheskaya Statistika , Novosibirsk : Nauka .
  • Darkhovsky , B. ( 2011 ). Optimal Sequential Tests for Testing Two Composite and Multiple Simple Hypotheses , Sequential Analysis 30 : 479 – 496 .
  • De , S. K. and Baron , M. ( 2012 ). Step-Up and Step-Down Methods for Testing Multiple Hypotheses in Sequential Experiments , Journal of Statistical Planning and Inference 142 : 2059 – 2070 .
  • Edwards , D. ( 1987 ). Extended-Paulson Sequential Selection , Annals of Statistics 15 : 449 – 455 .
  • Edwards , D. G. and Hsu , J. C. ( 1983 ). Multiple Comparisons with the Best Treatment , Journal of American Statistical Association 78 : 965 – 971 .
  • Glaspy , J. , Jadeja , J. S. , Justice , G. , Kessler , J. , Richards , D. , Schwartzberg , L. , Rigas , J. , Kuter , D. , Harmon , D. , Prow , D. , Demetri , G. , Gordon , D. , Arseneau , J. , Saven , A. , Hynes , H. , Boccia , R. , O'Byrne , J. , and Colowick , A. B. ( 2001 ). A Dose-Finding and Safety Study of Novel Erythropoiesis Stimulating Protein (NESP) for the Treatment of Anemia in Patients Receiving Multicycle Chemotherapy , British Journal of Cancer 84 : 17 – 23 .
  • Govindarajulu , Z. (1987). The Sequential Statistical Analysis of Hypothesis Testing, Point and Interval Estimation, and Decision Theory , Columbus : American Sciences Press.
  • Hamilton , D. C. and Lesperance , M. L. ( 1991 ). A Consulting Problem Involving Bivariate Acceptance Sampling by Variables , Canadian Journal of Statistics 19 : 109 – 117 .
  • Holm , S. ( 1979 ). A Simple Sequentially Rejective Multiple Test Procedure , Scandinavian Journal of Statistics 6 : 65 – 70 .
  • Hughes , M. D. ( 1993 ). Stopping Guidelines for Clinical Trials with Multiple Treatments , Statistics in Medicine 12 : 901 – 915 .
  • Jennison , C. and Turnbull , B. W. ( 1993 ). Group Sequential Tests for Bivariate Response: Interim Analyses of Clinical Trials with Both Efficacy and Safety Endpoints , Biometrics 49 : 741 – 752 .
  • Jennison , C. and Turnbull , B. W. ( 2000 ). Group Sequential Methods with Applications to Clinical Trials , Boca Raton : Chapman & Hall .
  • Lake , D. E. ( 2000 ). Minimum Chernoff Entropy and Exponential Bounds for Locating Changes , IEEE Transactions on Information Theory 46 : 1168 – 1170 .
  • Lange , N. , Ryan , L. , Billard , L. , Brillinger , D. , Conquest , L. , and Greenhouse , J. ( 1994 ). Case Studies in Biometry , New York : Wiley .
  • Lee , M.-L. T. ( 2004 ). Analysis of Microarray Gene Expression Data , Boston : Kluwer .
  • Novikov , A. ( 2009 ). Optimal Sequential Multiple Hypothesis Testing , Kybernetika 45 : 309 – 330 .
  • O'Brien , P. C. ( 1984 ). Procedures for Comparing Samples with Multiple Endpoints , Biometrics 40 : 1079 – 1087 .
  • Pocock , S. J. , Geller , N. L. , and Tsiatis , A. A. ( 1987 ). The Analysis of Multiple Endpoints in Clinical Trials , Biometrics 43 : 487 – 498 .
  • Sarkar , S. K. ( 2007 ). Step-up Procedures Controlling Generalized FWER and Generalized FDR , Annals of Statistics 35 : 2405 – 2420 .
  • Sidak , Z. ( 1967 ). Rectangular Confidence Regions for the Means of Multivariate Normal Distributions , Journal of American Statistical Association 62 : 626 – 633 .
  • Sobel , M. and Wald , A. ( 1949 ). A Sequential Decision Procedure for Choosing One of Three Hypotheses Concerning the Unknown Mean of a Normal Distribution , Annals of Mathematical Statistics 20 : 502 – 522 .
  • Tang , D.-I. and Geller , N. L. ( 1999 ). Closed Testing Procedures for Group Sequential Clinical Trials with Multiple Endpoints , Biometrics 55 : 1188 – 1192 .
  • Tartakovsky , A. G. , Li , X. R. , and Yaralov , G. ( 2003 ). Sequential Detection of Targets in Multichannel Systems , IEEE Transactions on Information Theory 49 : 425 – 445 .
  • Tartakovsky , A. G. and Veeravalli , V. V. ( 2004 ). Change-Point Detection in Multichannel and Distributed Systems with Applications , in Applications of Sequential Methodologies , N. Mukhopadhyay , S. Datta and S. Chattopadhyay , eds., pp. 339 – 370 , New York : Dekker .
  • Recommended by N. Mukhopadhyay

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.