68
Views
13
CrossRef citations to date
0
Altmetric
Original Articles

Optimal Biased Weighing Designs and Two-Level Main-Effect Plans

Pages 83-99 | Received 28 Mar 2012, Accepted 31 Oct 2012, Published online: 23 Dec 2013

References

  • Banerjee , T. and Mukerjee , R. 2008 . Optimal factorial designs for cDNA microarray experiments . Ann. Appl. Stat , 2 : 366 – 385 .
  • Ceranka , B. and Katulska , K. Relations between optimum biased spring balance weighing designs and optimum chemical balance weighing designs . Proc. l0th Conf. Probab. Math. Statist . Bratislava , Czechoslovakia . pp. 95 – 101 .
  • Ceranka , B. and Graczyk , M. 2009 . On some method of construction optimum biased spring balance weighing design . Colloq. Biometricum , 39 : 53 – 62 .
  • Chadjipantelis , T. , Kounias , S. and Moyssiadis , C. 1987 . The maximum determinant of 21 × 21 (+1, −1)-matrices and D-optimal designs . J. Stat. Plan. Inference , 16 : 167 – 178 .
  • Cheng , C. S. 1978 . Optimality of certain asymmetrical experimental designs . Ann. Stat , 6 : 1239 – 1261 .
  • Cheng , C. S. 1980 . Optimality of some weighing and 2 n fractional factorial designs . Ann. Stat , 8 : 436 – 446 .
  • Cheng , C. S. 1987a . An optimization problem with applications to optimal design theory . Ann. Stat , 15 : 712 – 723 .
  • Cheng , C. S. 1987b . An application of the Kiefer–Wolfowitz equivalence theorem to a problem in Hadamard transform optics . Ann. Stat , 15 : 1593 – 1603 .
  • Cheng , C. S. , Masaro , J. C. and Wong , C. S. 1985 . Optimal weighing designs . SIAM J. Alg. Disc. Methods , 6 : 259 – 267 .
  • Ehlich , H. 1964 . Determinantenabschatzungen furürbinare Matrizen . Math. Zeitschr , 83 : 123 – 132 .
  • Fan , K. 1954 . Inequalities for eigenvalues of Hermitian matrices . Nat. Bur. Standards Appl. Math. Ser , 39 : 131 – 139 .
  • Galil , Z. and Kiefer , J. 1980 . D-optimum weighing designs . Ann. Stat , 8 : 1293 – 1306 .
  • Galil , Z. and Kiefer , J. 1982 . Construction methods for D-optimum weighing designs when n ≡ 3 (mod 4) . Ann. Stat , 10 : 502 – 510 .
  • Glonek , G. F. V. and Solomon , P. J. 2004 . Factorial and time course designs for cDNA microarray experiments . Biostatistics , 5 : 89 – 111 .
  • Graczyk , M. 2011 . A-optimal biased spring balance weighing design . Kybernetika , 47 : 893 – 901 .
  • Harwit , M. and Sloane , N. J. A. 1979 . Hadamard transform optics , New York : Academic Press .
  • Hotelling , H. 1944 . Some improvements in weighing and other experimental techniques . Ann. Math. Stat , 15 : 297 – 306 .
  • Jacroux , M. and Notz , W. I. 1983 . On the optimality of spring balance weighing designs . Ann. Stat , 11 : 970 – 978 .
  • Jacroux , M. , Wong , C. S. and Masaro , J. C. 1983 . On the optimality of chemical balance weighing designs . J. Stat. Plan. Inference , 8 : 231 – 240 .
  • Kiefer , J. 1974 . General equivalence theory for optimum designs (approximate theory) . Ann. Stat , 2 : 849 – 879 .
  • Kiefer , J. 1975 . “ Optimality and construction of generalized Youden designs ” . In A survey of statistical designs and linear models , Edited by: Srivastava , J. N. 333 – 353 . Amsterdam , The Netherlands : North-Holland .
  • Kounias , S. and Chadjipantelis , T. 1983 . Some D-optimal weighing designs for n = 3 (mod 4) . J. Stat. Plan. Inference , 8 : 117 – 127 .
  • Kounias , S. and Farmakis , N. 1984 . A construction of D-optimal weighing designs when n = 3 mod 4 . J. Stat. Plan. Inference , 10 : 177 – 187 .
  • Marshall , A. W. and Olkin , I. 1979 . Inequalities: Theory of majorization and its applications , New York, NY : Academic Press .
  • Mukerjee , R. and Tang , B. 2012 . Optimal fractions of two-level factorials under a baseline parameterization . Biometrka , 99 : 71 – 84 .
  • Pukelsheim , F. 1989 . “ Complete class results for linear regression designs over the multi-dimensional cube ” . In Contributions to probability and statistics. Essays in honor of Ingram Olkin , Edited by: Gleser , L. J. , Perlman , M. D. , Press , S. J. and Sampson , A. R. 349 – 356 . New York : Springer .
  • Raghavarao , D. 1971 . Constructions and combinatorial problems in design of experiments , New York, NY : Wiley .
  • Shah , K. R. and Sinha , B. K. 1989 . Theory of optimal designs , New York, Springer .
  • Yang , C. H. 1966 . Some designs for maximizing (+1, −1) determinant of order n = 2 (mod 4) . Math. Comput , 20 : 147 – 148 .
  • Yang , C. H. 1968 . On designs of maximal (+1, −1) matrices of order n = 2 (mod 4) . Math. Comput , 22 : 174 – 180 .
  • Yang , Y. H. and Speed , T. 2002 . Design issues for cDNA microarray experiments . Nat. Genet. (Suppl.) , 3 : 579 – 588 .
  • Yates , F. 1935 . Complex experiments . J. R. Stat. Soc. Ser. B , 2 : 181 – 223 .

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.