Optimal discriminating designs for several competing regression models

The problem of constructing optimal designs for a class of regression models is considered. We investigate a version of the Tp-optimality criterion as introduced by Atkinson and Fedorov (1975b) and demonstrate that optimal designs with respect to this type of criteria can be obtained by solving (nonlinear) vector-valued approximation problems. We provide a characterization of the best approximations in this context and use these results to develop an efficient algorithm for the determination of the optimal discriminating designs. The results are illustrated by fnumerical examples.

[1]  Chiara Tommasi,et al.  Optimal designs for both model discrimination and parameter estimation , 2008 .

[2]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[3]  Anthony C. Atkinson,et al.  Examples of the use of an equivalence theorem in constructing optimum experimental designs for random-effects nonlinear regression models , 2008 .

[4]  Frank Bretz,et al.  Analysis of Dose–Response Studies—Modeling Approaches , 2006 .

[5]  A. Atkinson,et al.  The design of experiments for discriminating between two rival models , 1975 .

[6]  Anthony C. Atkinson,et al.  DT-optimum designs for model discrimination and parameter estimation , 2008 .

[7]  J. López–Fidalgo,et al.  An optimal experimental design criterion for discriminating between non‐normal models , 2007 .

[8]  Weng Kee Wong,et al.  ON THE CONSTRUCTION OF Grm-OPTIMAL DESIGNS , 1999 .

[9]  W. J. Studden.  Some Robust-Type D-Optimal Designs in Polynomial Regression , 1982 .

[10]  A. Atkinson,et al.  Optimal design : Experiments for discriminating between several models , 1975 .

[11]  D. Ucinski,et al.  T‐optimum designs for discrimination between two multiresponse dynamic models , 2005 .

[12]  Valerii V. Fedorov,et al.  Duality of optimal designs for model discrimination and parameter estimation , 1986 .

[13]  V. Melas,et al.  T-optimal designs for discrimination between two polynomial models , 2012, 1205.6283.

[14]  Holger Dette,et al.  Optimal discrimination designs , 2009, 0908.1912.

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

[16]  Holger Dette.  Discrimination designs for polynomial regression on compact intervals , 1994 .

[17]  G. Meinardus.  Approximation of Functions: Theory and Numerical Methods , 1967 .

[18]  I. Singer.  Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces , 1970 .

[19]  Holger Dette,et al.  Optimal Designs for Dose-Finding Studies , 2008 .

[20]  Holger Dette,et al.  Optimal designs for the identification of the order of a Fourier regression , 1998 .

[21]  J. Kiefer.  General Equivalence Theory for Optimum Designs (Approximate Theory) , 1974 .

[22]  F Bretz,et al.  Combining Multiple Comparisons and Modeling Techniques in Dose‐Response Studies , 2005, Biometrics.

[23]  Stephen M. Stigler,et al.  Optimal Experimental Design for Polynomial Regression , 1971 .

[24]  D. Wiens.  Robust discrimination designs , 2009 .

[25]  M. Zen,et al.  SOME CRITERION-ROBUST OPTIMAL DESIGNS FOR THE DUAL PROBLEM OF MODEL DISCRIMINATION AND PARAMETER ESTIMATION , 2002 .

[26]  Mei-Mei Zen,et al.  Criterion-robust optimal designs for model discrimination and parameter estimation in Fourier regression models , 2004 .

[27]  Andrej Pázman,et al.  Nonlinear Regression , 2019, Handbook of Regression Analysis With Applications in R.

[28]  Chiara Tommasi,et al.  Bayesian optimum designs for discriminating between models with any distribution , 2010, Comput. Stat. Data Anal..