LEADER 03768nam 2200577Ia 450 001 9910437873103321 005 20200520144314.0 010 $a1-4614-6363-7 024 7 $a10.1007/978-1-4614-6363-4 035 $a(CKB)2550000001044169 035 $a(EBL)1205309 035 $a(SSID)ssj0000880308 035 $a(PQKBManifestationID)11542523 035 $a(PQKBTitleCode)TC0000880308 035 $a(PQKBWorkID)10873491 035 $a(PQKB)10542214 035 $a(DE-He213)978-1-4614-6363-4 035 $a(MiAaPQ)EBC1205309 035 $a(PPN)169136140 035 $a(EXLCZ)992550000001044169 100 $a20130201d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDesign of experiments in nonlinear models $easymptotic normality, optimality criteria and small-sample properties /$fLuc Pronzato 205 $a1st ed. 2013. 210 $aNew York $cSpringer$d2013 215 $a1 online resource (399 p.) 225 1 $aLecture Notes in Statistics,$x0930-0325 ;$v212 300 $aDescription based upon print version of record. 311 $a1-4614-6362-9 320 $aInclude bibliographical references and index. 327 $aIntroduction -- Asymptotic designs and uniform convergence. Asymptotic properties of the LS estimator -- Asymptotic properties of M, ML and maximum a posteriori estimators -- Local optimality criteria based on asymptotic normality -- Criteria based on the small-sample precision of the LS estimator -- Identifiability, estimability and extended optimality criteria -- Nonlocal optimum design -- Algorithms?a survey -- Subdifferentials and subgradients -- Computation of derivatives through sensitivity functions -- Proofs -- Symbols and notation -- List of labeled assumptions -- References. 330 $aDesign of Experiments in Nonlinear Models: Asymptotic Normality, Optimality Criteria and Small-Sample Properties provides a comprehensive coverage of the various aspects of experimental design for nonlinear models. The book contains original contributions to the theory of optimal experiments that will interest students and researchers in the field. Practitionners motivated by applications will find valuable tools to help them designing their experiments.  The first three chapters expose the connections between the asymptotic properties of estimators in parametric models and experimental design, with more emphasis than usual on some particular aspects like the estimation of a nonlinear function of the model parameters, models with heteroscedastic errors, etc. Classical optimality criteria based on those asymptotic properties are then presented thoroughly in a special chapter.  Three chapters are dedicated to specific issues raised by nonlinear models. The construction of design criteria derived from non-asymptotic considerations (small-sample situation) is detailed. The connection between design and identifiability/estimability issues is investigated. Several approaches are presented to face the problem caused by the dependence of an optimal design on the value of the parameters to be estimated.  A survey of algorithmic methods for the construction of optimal designs is provided. 410 0$aLecture Notes in Statistics,$x0930-0325 ;$v212 606 $aExperimental design 606 $aNonlinear difference equations 615 0$aExperimental design. 615 0$aNonlinear difference equations. 676 $a519.5 676 $a519.57 700 $aPronzato$b Luc$023100 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910437873103321 996 $aDesign of Experiments in Nonlinear Models$92504201 997 $aUNINA