Optimum design for ill-conditioned models: K–optimality and stable parameterizations

Chemometrics and Intelligent Laboratory Systems - Tập 239 - Trang 104874 - 2023
Belmiro P.M. Duarte1,2, Anthony C. Atkinson3, Nuno M.C. Oliveira2
1Polytechnic Institute of Coimbra, ISEC, Department of Chemical & Biological Engineering, Rua Pedro Nunes, 3030–199 Coimbra, Portugal
2University of Coimbra, CIEPQPF, Department of Chemical Engineering, Rua Sílvio Lima — Pólo II, 3030–790 Coimbra, Portugal
3Department of Statistics, London School of Economics, London WC2A 2AE, United Kingdom

Tài liệu tham khảo

Seber, 2003 López, 2015, Nonlinear ill-posed problem analysis in model-based parameter estimation and experimental design, Comput. Chem. Eng., 77, 24, 10.1016/j.compchemeng.2015.03.002 Baty, 2015, A toolbox for nonlinear regression in R: the package nlstools, J. Stat. Softw., 66, 1, 10.18637/jss.v066.i05 Huet, 2004 Celminš, 1981, Least square model fitting with transformation of variable, J. Stat. Comput. Simul., 14, 17, 10.1080/00949658108810516 Kutner, 1996 Box, 1964, An analysis of transformations, J. R. Stat. Soc. Ser. B Stat. Methodol., 26, 211 Golub, 1973, The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate, SIAM J. Numer. Anal., 10, 413, 10.1137/0710036 Ross, 1970, The efficient use of function minimization in non-linear maximum-likelihood estimation, J. R. Stat. Soc. Ser. C. Appl. Stat., 19, 205 Tsai, 1988, Power transformations and reparameterizations in nonlinear regression models, Technometrics, 30, 441, 10.1080/00401706.1988.10488440 Chen, 1995, Transformations for improving linearization confidence intervals in nonlinear regression, J. Amer. Statist. Assoc., 90, 1271, 10.1080/01621459.1995.10476631 Atkinson, 2021, The Box-Cox transformation: review and extensions, Statist. Sci., 36, 239, 10.1214/20-STS778 Schwaab, 2008, Optimum reparameterization of power function models, Chem. Eng. Sci., 63, 4631, 10.1016/j.ces.2008.07.005 Ross, 2010, Reparameterization of nonlinear statistical models: a case study, J. Appl. Stat., 37, 2015, 10.1080/02664760903207332 Yue, 2022, Constructing K-optimal designs for regression models, Statist. Papers, 1 Xu, 2013, Experimental quality evaluation of lattice basis reduction methods for decorrelating low-dimensional integer least squares problems, EURASIP J. Adv. Signal Process., 2013, 1, 10.1186/1687-6180-2013-137 Ben-Tal, 2001 Boyd, 2004 Sagnol, 2013, On the semidefinite representation of real functions applied to symmetric matrices, Linear Algebra Appl., 439, 2829, 10.1016/j.laa.2013.08.021 Vandenberghe, 1999, Applications of semidefinite programming, Appl. Numer. Math., 29, 283, 10.1016/S0168-9274(98)00098-1 Duarte, 2015, Finding Bayesian optimal designs for nonlinear models: A semidefinite programming-based approach, Internat. Statist. Rev., 83, 239, 10.1111/insr.12073 Ye, 2013, Minimizing the condition number to construct design points for polynomial regression models, SIAM J. Optim., 23, 666, 10.1137/110850268 Ye, 1997 Ross, 1990 Wolfram Research, Inc., 2022 Pukelsheim, 1992, Efficient rounding of approximate designs, Biometrika, 79, 763, 10.1093/biomet/79.4.763 Nielsen, 2010, 176 Marquardt, 1970, Generalized inverses, ridge regression, biased linear estimation, and nonlinear estimation, Technometrics, 12, 591, 10.2307/1267205 Belsley, 2005 Rempel, 2014, On exact K-optimal designs minimizing the condition number, Comm. Statist. Theory Methods, 43, 1114, 10.1080/03610926.2012.670352 Marco, 2010, Polynomial least squares fitting in the Bernstein basis, Linear Algebra Appl., 433, 1254, 10.1016/j.laa.2010.06.031 Brubeck, 2021, Vandermonde with Arnoldi, SIAM Rev., 63, 405, 10.1137/19M130100X Hill, 1910, The possible effects of the aggregation of the molecules of hæmoglobin on its dissociation curves, J. Physiol., 40, i Grant, 2012 Andersen, 2009 Vandenberghe, 1996, Semidefinite programming, SIAM Rev., 8, 49, 10.1137/1038003