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Volumn 136, Issue 3, 2006, Pages 1135-1152

Designs in nonlinear regression by stochastic minimization of functionals of the mean square error matrix

Author keywords

A and D optimality; Distribution of estimators; Mean square error; Method of stochastic optimization; Nonlinear least squares

Indexed keywords


EID: 28044466420     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2004.08.015     Document Type: Article
Times cited : (7)

References (29)
  • 2
    • 0028080154 scopus 로고
    • A dynamic approach to predicting bacterial growth in food
    • J. Baranyi T.A. Roberts A dynamic approach to predicting bacterial growth in food Internat. J. Food Microbiol. 23 1994 277-294
    • (1994) Internat. J. Food Microbiol. , vol.23 , pp. 277-294
    • Baranyi, J.1    Roberts, T.A.2
  • 5
    • 0037061040 scopus 로고    scopus 로고
    • Optimal temperature input design for estimation of the square root model parameters: Parameters accuracy and model validity restrictions
    • K. Bernaerts R.D. Servaes S. Kooyman K.J. Versyck J.F. Van Impe Optimal temperature input design for estimation of the square root model parameters: Parameters accuracy and model validity restrictions Internat. J. Food Microbiol. 73 2002 145-157
    • (2002) Internat. J. Food Microbiol. , vol.73 , pp. 145-157
    • Bernaerts, K.1    Servaes, R.D.2    Kooyman, S.3    Versyck, K.J.4    Van Impe, J.F.5
  • 6
    • 0000792515 scopus 로고
    • Multidimensional stochastic approximation methods
    • J.R. Blum Multidimensional stochastic approximation methods Ann. Math. Statist. 25 1954 737-744
    • (1954) Ann. Math. Statist. , vol.25 , pp. 737-744
    • Blum, J.R.1
  • 7
    • 0036568358 scopus 로고    scopus 로고
    • Constrained design strategies for improving normal approximations in nonlinear regression problems
    • M. Clyde K. Chaloner Constrained design strategies for improving normal approximations in nonlinear regression problems J. Statist. Plann. Inference 104 1 2002 175-196
    • (2002) J. Statist. Plann. Inference , vol.104 , Issue.1 , pp. 175-196
    • Clyde, M.1    Chaloner, K.2
  • 9
    • 0346968368 scopus 로고    scopus 로고
    • Standardized maximin E-optimal designs for the Michaelis-Menten model
    • H. Dette V.B. Melas A. Pepelyshev Standardized maximin E-optimal designs for the Michaelis-Menten model Statist. Sinica 13 2003 1147-1163
    • (2003) Statist. Sinica , vol.13 , pp. 1147-1163
    • Dette, H.1    Melas, V.B.2    Pepelyshev, A.3
  • 10
    • 0042859914 scopus 로고    scopus 로고
    • Accelerated randomized stochastic optimization
    • J. Dipon Accelerated randomized stochastic optimization Ann. Statist. 31 4 2003 1260-1281
    • (2003) Ann. Statist. , vol.31 , Issue.4 , pp. 1260-1281
    • Dipon, J.1
  • 11
    • 0003219216 scopus 로고
    • Stochastic approximation of minima with improved asymptotic speed
    • V. Fabian Stochastic approximation of minima with improved asymptotic speed Ann. Math. Statist. 38 1967 191-200
    • (1967) Ann. Math. Statist. , vol.38 , pp. 191-200
    • Fabian, V.1
  • 12
    • 0001214703 scopus 로고
    • On asymptotic normality in stochastic approximation
    • V. Fabian On asymptotic normality in stochastic approximation Ann. Math. Statist. 39 1968 1327-1332
    • (1968) Ann. Math. Statist. , vol.39 , pp. 1327-1332
    • Fabian, V.1
  • 13
    • 4143055041 scopus 로고
    • On the choice of design in stochastic approximation methods
    • V. Fabian On the choice of design in stochastic approximation methods Ann. Math. Statist. 39 1968 457-465
    • (1968) Ann. Math. Statist. , vol.39 , pp. 457-465
    • Fabian, V.1
  • 14
    • 0024606752 scopus 로고
    • Recent advances in nonlinear experimental design
    • I. Ford C.P. Kitsos D.M. Titterington Recent advances in nonlinear experimental design Technometrics 31 1 1989 49-60
    • (1989) Technometrics , vol.31 , Issue.1 , pp. 49-60
    • Ford, I.1    Kitsos, C.P.2    Titterington, D.M.3
  • 15
    • 28044450869 scopus 로고    scopus 로고
    • Distribution of the least squares estimator, stochastic optimization and optimum designs in nonlinear models
    • Technical Report No. 2003-7, National Institute of Agricultural Research (INRA). Biometrics Unit, Jouy-en-Josas, France
    • Gauchi, J.-P., Pázman, A., 2003. Distribution of the least squares estimator, stochastic optimization and optimum designs in nonlinear models. Technical Report No. 2003-7, National Institute of Agricultural Research (INRA). Biometrics Unit, Jouy-en-Josas, France.
    • (2003)
    • Gauchi, J.-P.1    Pázman, A.2
  • 16
    • 0002803115 scopus 로고
    • Accelerated stochastic approximation method
    • H. Kesten Accelerated stochastic approximation method Ann. Math. Statist. 29 1 1958 41-59
    • (1958) Ann. Math. Statist. , vol.29 , Issue.1 , pp. 41-59
    • Kesten, H.1
  • 17
    • 28044434196 scopus 로고
    • Almost exact distributions of estimators I + II
    • A. Pázman Almost exact distributions of estimators I + II Statistics 21 1990 1-33
    • (1990) Statistics , vol.21 , pp. 1-33
    • Pázman, A.1
  • 18
    • 28044449730 scopus 로고
    • Geometry of the nonlinear regression with prior
    • A. Pázman Geometry of the nonlinear regression with prior Acta Math. Univ. Comenian. LXI 1992 263-267
    • (1992) Acta Math. Univ. Comenian. , vol.61 , pp. 263-267
    • Pázman, A.1
  • 19
    • 24444476240 scopus 로고
    • Higher dimensional nonlinear regression - A statistical use of the Riemannian curvature tensor
    • A. Pázman Higher dimensional nonlinear regression - a statistical use of the Riemannian curvature tensor Statistics 25 1993 17-25
    • (1993) Statistics , vol.25 , pp. 17-25
    • Pázman, A.1
  • 21
    • 0001438957 scopus 로고
    • Nonlinear experimental design based on the distribution of estimators
    • A. Pázman L. Pronzato Nonlinear experimental design based on the distribution of estimators J. Statist. Plann. Inference 33 1992 385-402
    • (1992) J. Statist. Plann. Inference , vol.33 , pp. 385-402
    • Pázman, A.1    Pronzato, L.2
  • 22
    • 0002015332 scopus 로고
    • Stepsize rules, stopping times and their implementation in stochastic quasigradient algorithms
    • Yu. Ermoliev R.J.-B. Wets (Eds.) Springer Berlin
    • G.Ch. Pflug Stepsize rules, stopping times and their implementation in stochastic quasigradient algorithms. In: Yu. Ermoliev R.J.-B. Wets (Eds.) Numerical Techniques for Stochastic Optimization 1988 Springer Berlin
    • (1988) Numerical Techniques for Stochastic Optimization
    • Pflug, G.Ch.1
  • 23
    • 0001645072 scopus 로고
    • Non-asymptotic confidence bounds for stochastic approximation algorithms with constant step size
    • G.Ch. Pflug Non-asymptotic confidence bounds for stochastic approximation algorithms with constant step size Mh. Math. 110 1990 297-314
    • (1990) Mh. Math. , vol.110 , pp. 297-314
    • Pflug, G.Ch.1
  • 25
    • 84904772278 scopus 로고
    • Pseudogradient adaptation and training algorithms
    • B.T. Polyak Ya.Z. Tsypkin Pseudogradient adaptation and training algorithms Automat. Remote Control 34 3, part 1 1973 377-397
    • (1973) Automat. Remote Control , vol.34 , Issue.3 PART 1 , pp. 377-397
    • Polyak, B.T.1    Tsypkin, Ya.Z.2
  • 26
    • 0022093313 scopus 로고
    • Robust experimental design via stochastic approximation
    • L. Pronzato E. Walter Robust experimental design via stochastic approximation Math. Biosci. 75 1985 103-120
    • (1985) Math. Biosci. , vol.75 , pp. 103-120
    • Pronzato, L.1    Walter, E.2
  • 29
    • 28044460292 scopus 로고
    • Exact experimental designs via stochastic optimization for nonlinear regression models
    • Physica-Verlag Heidelberg
    • Vila, J.P., 1990, Exact experimental designs via stochastic optimization for nonlinear regression models. Compstat Proceedings for IASC (International Association for Statistical Computing), 1990. Physica-Verlag Heidelberg. pp. 291-296.
    • (1990) Compstat Proceedings for IASC (International Association for Statistical Computing) , pp. 291-296
    • Vila, J.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.