Max–min optimal discriminating designs for several statistical models

In the literature, different optimality criteria have been considered for model identification. Most of the proposals assume the normal distribution for the response variable and thus they provide optimality criteria for discriminating between regression models. In this paper, a max–min approach is followed to discriminate among competing statistical models (i.e., probability distribution families). More specifically, k different statistical models (plausible for the data) are embedded in a more general model, which includes them as particular cases. The proposed optimal design maximizes the minimum KL-efficiency to discriminate between each rival model and the extended one. An equivalence theorem is proved and an algorithm is derived from it, which is useful to compute max–min KL-efficiency designs. Finally, the algorithm is run on two illustrative examples.

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

[2]  Caterina May,et al.  An adaptive sequential optimum design for model selection and parameter estimation in non-linear nested models , 2011, 1107.5253.

[3]  Chiara Tommasi,et al.  Optimal Designs for Discriminating among Several Non-Normal Models , 2007 .

[4]  Paula Camelia Trandafir,et al.  Optimal designs for discriminating between some extensions of the Michaelis–Menten model , 2005 .

[5]  D. Cox,et al.  Planning Experiments for Discriminating between Models , 1974 .

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

[7]  Optimal Discrimination Designs for Exponential Regression Models , 2007 .

[8]  Anthony C. Atkinson,et al.  Planning experiments to detect inadequate regression models , 1972 .

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

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

[11]  Douglas E. Barker,et al.  Comparison of six particle size distribution models on the goodness-of-fit to particulate matter sampled from animal buildings , 2012, Journal of the Air & Waste Management Association.

[12]  E. Stacy.  A Generalization of the Gamma Distribution , 1962 .

[13]  Anthony C. Atkinson,et al.  The Design of Experiments to Discriminate Between Two Rival Generalized Linear Models , 1992 .

[14]  Holger Dette,et al.  Efficient design of experiments in the Monod model , 2003 .

[15]  Discrimination Between Random and Fixed Effect Logistic Regression Models , 2010 .

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

[17]  H. Dette,et al.  Optimal designs for discriminating between dose-response models in toxicology studies , 2010, 1011.5747.

[18]  Christian Bauckhage,et al.  Computing the Kullback-Leibler Divergence between two Generalized Gamma Distributions , 2014, ArXiv.

[19]  Dariusz Ucinski,et al.  T -Optimum Designs for Multiresponse Dynamic Heteroscedastic Models , 2004 .

[20]  Steven E. Rigdon,et al.  Model-Oriented Design of Experiments , 1997, Technometrics.

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

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

[23]  Holger Dette,et al.  Optimal discriminating designs for several competing regression models , 2013, 1306.1320.