On Exact K-optimal Designs Minimizing the Condition Number

References

• Angelis , L. , Bora-Senta , E. , Moyssiadis , C. ( 2001 ). Optimal exact experimental designs with correlated errors through a simulated annealing algorithm . Computat. Statist. Data Anal. 37 : 275 – 296 .
   Web of Science ®Google Scholar
• Brooks , S. P. , Morgan , B. J. T. ( 1995 ). Optimization using simulated annealing . Statistician 44 : 241 – 257 .
   Google Scholar
• Chen , X. , Womersley , R. S. , Ye , J. J. ( 2011 ). Minimizing the condition number of a gram matrix . SIAM J. Optimiz. 21 : 127 – 148 .
   Web of Science ®Google Scholar
• Elliot , L. J. , Eccleston , J. A. , Martin , R. J. ( 1999 ). An algorithm for the design of factorial experiments when the data are correlated . Statist. Comput. 9 : 195 – 201 .
   Web of Science ®Google Scholar
• Fang , Z. , Wiens , D. P. ( 2000 ). Integer-valued minimax robust designs for estimation and extrapolation in heteroscedastic, approximately linear models . J. Amer. Statist. Assoc. 95 : 807 – 818 .
   Web of Science ®Google Scholar
• Givens , G. H. , Hoeting , J. A. ( 2005 ). Computational Statistics . Hoboken, New Jersey : Wiley .
   Google Scholar
• Haines , L. M. ( 1987 ). The application of the annealing algorithm to the construction of the exact optimal designs for linear regression models . Technometrics 29 : 439 – 447 .
   Web of Science ®Google Scholar
• Horn , R. , Johnson , C. ( 1985 ). Matrix Analysis . Cambridge : Cambridge University Press .
   Google Scholar
• Montgomery , D. C. , Peck , E. A. , Vining , G. G. ( 2006 ). Introduction to Linear Regression Analysis. ed. , 4th , Hoboken, New Jersey : Wiley .
   Google Scholar
• Mukerjee , R. , Wu , C. F. J. ( 2006 ). A Modern Theory of Factorial Designs . New York : Springer .
   Google Scholar
• Pukelsheim , F. ( 1993 ). Optimal Design of Experiments . New York : Wiley .
   Google Scholar
• Schervish , M. J. (1995). Theory of Statistics . New York : Springer-Verlag.
   Google Scholar
• Shi , P. , Ye , J. , Zhou , J. ( 2007 ). Discrete minimax designs for regression models with autocorrelated MA errors . J. Statist. Plann. Infer. 137 : 2721 – 2731 .
   Web of Science ®Google Scholar
• Tang , B. , Deng , L. ( 1999 ). Minimum G 2-Aberration for nonregular fractional factorial designs . Ann. Statist. 27 : 1914 – 1926 .
   Web of Science ®Google Scholar
• Wilmut , M. , Zhou , J. ( 2011 ). D-optimal minimax design criterion for two-level fractional factorial designs . J. Statist. Plann. Infer. 141 : 576 – 587 .
   Web of Science ®Google Scholar
• Ye , J. , Zhou , J. ( 2011 ). Minimizing the condition number to construct design points for polynomial regression models . Preprint .
   Google Scholar
• Zhou , J. ( 2001 ). Integer-valued, minimax robust designs for approximately linear models with correlated errors . Commun. Statist. Theor. Meth. 30 : 21 – 39 .
   Web of Science ®Google Scholar
• Zhou , J. ( 2008 ). D-optimal minimax regression designs on discrete design space . J. Statist. Plann. Infer. 138 : 4081 – 4092 .
   Web of Science ®Google Scholar
• Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lsta.
   Google Scholar