MODEL SELECTION AND PARAMETER ESTIMATION IN NON-LINEAR NESTED MODELS: A SEQUENTIAL GENERALIZED DKL-OPTIMUM DESIGN

This work proposes a sequential procedure which is useful to select the best model among several nested non-linear models and to estimate eciently the parameters of the chosen model. At the rst step of this procedure, a generalized DKL-optimum design is computed, which is optimal for the double goal of model selection and parameter estimation. Subsequently, at each following step, an adaptive generalized DKL-optimum design is computed on the base of the data accrued and tests previously performed. The proposed sequential scheme selects the best non-linear model with probability converging to one; moreover it estimates eciently its parameters, since the adaptive sequential DKL-optimum designs converge to the D-optimum design for the \true" model.

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

[2]  R. Tyrrell Rockafellar,et al.  Convex Analysis , 1970, Princeton Landmarks in Mathematics and Physics.

[3]  Holger Dette,et al.  Constrained D- and D1-optimal designs for polynomial regression , 2000 .

[4]  David Williams,et al.  Probability with Martingales , 1991, Cambridge mathematical textbooks.

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

[6]  R. Bass,et al.  Review: P. Billingsley, Convergence of probability measures , 1971 .

[7]  Kengo Kato,et al.  Asymptotics for argmin processes: Convexity arguments , 2009, J. Multivar. Anal..

[8]  H. Dette,et al.  Efficient experimental designs for sigmoidal growth models , 2005 .

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

[10]  Holger Dette,et al.  Robust designs for polynomial regression by maximizing a minimum of D- and D1-efficiencies , 2001 .

[11]  H. Chernoff.  Approaches in Sequential Design of Experiments , 1973 .

[12]  Robin Sibson,et al.  Optimal Design: An Introduction to the Theory for Parameter Estimation. , 1982 .

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

[14]  D. M. Titterington,et al.  Recent advances in nonlinear experiment design , 1989 .

[15]  Anthony C. Atkinson,et al.  Optimum Experimental Designs, with SAS , 2007 .

[16]  Arthur B. Yeh,et al.  A two-stage strategy for the construction of D-optimal experimental designs , 1998 .

[17]  T. Ferguson.  A Course in Large Sample Theory , 1996 .

[18]  Atanu Biswas,et al.  An efficient design for model discrimination and parameter estimation in linear models , 2002 .

[19]  W. J. Hill,et al.  A Joint Design Criterion for the Dual Problem of Model Discrimination and Parameter Estimation , 1968 .

[20]  Jean-Paul Chilès,et al.  Wiley Series in Probability and Statistics , 2012 .

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

[22]  Drew Seils,et al.  Optimal design , 2007 .

[23]  Andrej Pázman,et al.  Foundations of Optimum Experimental Design , 1986 .

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

[25]  Holger Dette,et al.  Constrained D- and D1-optimal designs for polynomial regression , 2000 .

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

[27]  S. Silvey.  Optimal Design: An Introduction to the Theory for Parameter Estimation , 1980 .

[28]  Holger Dette,et al.  On a mixture of the D- and D1-optimality criterion in polynomial regression , 1993 .

[29]  Alison L Gibbs,et al.  On Choosing and Bounding Probability Metrics , 2002, math/0209021.

[30]  A comparison of sequential and non-sequential designs for discrimination between nested regression models , 2004 .

[31]  Mei-Mei Zen,et al.  Criterion-robust optimal designs for model discrimination and parameter estimation: Multivariate polynomial regression case , 2004 .

[32]  Holger Dette,et al.  Optimal Design for Goodness-of-Fit of the Michaelis–Menten Enzyme Kinetic Function , 2005 .

[33]  David M. Borth,et al.  A Total Entropy Criterion for the Dual Problem of Model Discrimination and Parameter Estimation , 1975 .

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

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

[36]  H. White.  Maximum Likelihood Estimation of Misspecified Models , 1982 .