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Original Articles

Applications of a probability inequality to ranking and selection and other related problems

Pages 1105-1120 | Published online: 27 Jun 2007

References

  • Bechhofer , K. L. 1954 . A single-stage multiple deci sion procedure for ranking means of normal popu lations with known variances . Ann. Math. Statist. , 25 : 16 – 39 .
  • Bechhofer , R. E. , Kiefer , J. , Sobel , M. , Littlewood , J. E. and Pólya , G. 1968 . “ Institute of Mathematical Statistics Research Monograph ” . In Sequential Identification and Ranking Procedures , Series III Chicago : Chicago University Press .
  • Dunnett , C. W. and Sobel , M. 1954 . Approximations to the probability integral and certain percentage points of a multivariate analogue of Student’s t-distribution . Biometrika , 42 : 258 – 260 .
  • Gupta , S. S. 1963a . On a selection and ranking procedure for gamma populations . Ann. Inst. Statist. Math. , 14 : 199 – 216 .
  • Gupta , S. S. 1963b . Probability integrals of multivariate normal and multivariate t . Ann. Math. Statist. , 34 : 797 – 828 .
  • Gupta , S. S. and Panchapakesan , S. 1972 . On a class of subset selection procedures . Ann. Math. Statist. , 43 : 814 – 822 .
  • Hardy , G. H. , Littlewood , J. E. and Pólya , G. 1959 . Inequalities , 2nd ed. , Cambridge : Cambridge University Press .
  • Kimball , A. W. 1951 . On dependent tests of significance in the analysis of variance . Ann. Math. Statist. , 22 : 600 – 602 .
  • Loève , M. 1963 . Probability Theory , Princeton : D. Van Nostrand Co. Inc. .
  • Marshall , A. W. and Olkin , I. 1974 . Majorization in multivariate distributions . Ann. Statist. , 2 : 1189 – 1200 .
  • Miller , R. G. 1966 . Simultaneous Statistical Inference , New York : McGraw-Hill, Inc. .
  • Ramberg , J. S. 1972 . Selection sample size approximations . Ann. Math. Statist. , 43 : 1977 – 1980 .
  • Šidák , Z. 1973 . A chain of inequalities for some types of multivariate distributions, with nine special cases . Aplik. Mat. , 18 : 110 – 118 .
  • Tong , Y. L. 1970 . Some probability inequalities of multivariate normal and multivariate t . J. Amer. Statist. Assoc. , 65 : 1243 – 1247 .
  • Tong , Y. L. 1972 . On the consistency of single-stage ranking procedures . Ann. Inst. Statist. Math. , 24 : 271 – 284 .
  • Tong , Y. L. 1977 . An ordering theorem for conditionally independent and identically distributed random variables . Ann. Statist. , 5 : 274 – 277 .

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