caa a22 4500 475826604 CHVBK 20180406123830.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1023/A:1004137906908 doi (NATIONALLICENCE)springer-10.1023/A:1004137906908 A Unified Approach to Second Order Optimality Criteria in Nonlinear Design of Experiments [Elektronische Daten] [Holger Dette, Yuri Grigoriev] In the nonlinear regression model we consider the optimal design problem with a second order design D-criterion. Our purpose is to present a general approach to this problem, which includes the asymptotic second order bias and variance criterion of the least squares estimator and criteria using the volume of confidence regions based on different statistics. Under assumptions of regularity for these statistics a second order approximation of the volume of these regions is derived which is proposed as a quadratic optimality criterion. These criteria include volumes of confidence regions based on the u n - representable statistics. An important difference between the criteria presented in this paper and the second order criteria commonly employed in the recent literature is that the former criteria are independent of the vector of residuals. Moreover, a refined version of the commonly applied criteria is obtained, which also includes effects of nonlinearity caused by third derivatives of the response function. The Institute of Statistical Mathematics, 2000 D -optimal design nationallicence nonlinear regression model nationallicence second order approximation nationallicence asymptotic expansion nationallicence Dette Holger Fakultät für Mathematik, Ruhr-Universität Bochum, 44780, Bochum, Germany aut Grigoriev Yuri Fakultät für Angewandte Mathematik, Technische Universität, 630092, Novosibirsk, Russian Federation aut Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/3(2000-09-01), 574-597 0020-3157 52:3<574 2000 52 10463 https://doi.org/10.1023/A:1004137906908 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1004137906908 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dette Holger Fakultät für Mathematik, Ruhr-Universität Bochum, 44780, Bochum, Germany aut NATIONALLICENCE 700 1- Grigoriev Yuri Fakultät für Angewandte Mathematik, Technische Universität, 630092, Novosibirsk, Russian Federation aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/3(2000-09-01), 574-597 0020-3157 52:3<574 2000 52 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer