A note on $$R$$-optimal designs for multiresponse models

This paper considers the optimal design problem for multiresponse regression models. The $$R$$-optimality introduced by Dette (J R Stat Soc B 59:97–110, 1997) for single response experiments is extended to the case of multiresponse parameter estimation. A general equivalence theorem for the $$R$$-optimality is provided for multiresponse models. Illustrative examples of the $$R$$-optimal designs for two multiresponse models are presented based on the general equivalence theorem.

[1]  Holger Dette,et al.  Designing Experiments with Respect to ‘Standardized’ Optimality Criteria , 1997 .

[2]  H. Dette.  Elfving's Theorem for $D$-Optimality , 1993 .

[3]  W. G. Hunter,et al.  Design of experiments for parameter estimation in multiresponse situations , 1966 .

[4]  Abbas Seifi,et al.  Optimal design of multi-response experiments using semi-definite programming , 2009 .

[5]  O. Krafft,et al.  D-optimal designs for a multivariate regression model , 1992 .

[6]  Lorens A. Imhof,et al.  Optimum Designs for a Multiresponse Regression Model , 2000 .

[7]  W. Wong,et al.  OPTIMAL DESIGNS FOR PARALLEL MODELS WITH CORRELATED RESPONSES , 2006 .

[8]  M. Deaton,et al.  Response Surfaces: Designs and Analyses , 1989 .

[9]  H. Dette.  A new interpretation of optimality forE-optimal designs in linear regression models , 1993 .

[10]  P. Whittle.  Some General Points in the Theory of Optimal Experimental Design , 1973 .

[11]  Xin Liu,et al.  ILr-optimal designs for a hierarchically ordered system of regression models , 2010, Comput. Stat. Data Anal..

[12]  Holger Dette,et al.  Optimality criteria for regression models based on predicted variance , 1999 .

[13]  Holger Dette,et al.  A Geometric Solution of the Bayesian E-Optimal Design Problem , 1994 .

[14]  T. Holland-Letz,et al.  A geometric characterization of c-optimal designs for heteroscedastic regression , 2009, 0911.3801.

[15]  Fred J. Hickernell,et al.  OPTIMALITY CRITERIA FOR MULTIRESPONSE LINEAR MODELS BASED ON PREDICTIVE ELLIPSOIDS , 2010 .

[16]  W. J. Studden,et al.  Theory Of Optimal Experiments , 1972 .

[17]  Dennis K. J. Lin,et al.  Optimal designs for dual response polynomial regression models , 2001 .