메뉴 건너뛰기




Volumn 21, Issue 3, 1996, Pages 273-292

Some applications of Stieltjes transforms in the construction of optimal designs for nonlinear regression models

Author keywords

Approximate design theory; Bayesian D optimal design; Continued fractions

Indexed keywords

APPROXIMATION THEORY; COMPUTATION THEORY; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; NUMERICAL METHODS; OPTIMIZATION; PROBABILITY; PRODUCT DESIGN; REGRESSION ANALYSIS;

EID: 0030109589     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-9473(95)00015-1     Document Type: Article
Times cited : (6)

References (31)
  • 2
    • 0002419565 scopus 로고
    • Design of experiments in non-linear situations
    • Box, G.E.P. and H. Lucas, Design of experiments in non-linear situations, Biometrika, 46 (1959) 77-90.
    • (1959) Biometrika , vol.46 , pp. 77-90
    • Box, G.E.P.1    Lucas, H.2
  • 3
    • 0000626524 scopus 로고
    • Expected information as expected utility
    • Bernado, J.M., Expected information as expected utility, Ann. Statist., 7 (1979) 686-690.
    • (1979) Ann. Statist. , vol.7 , pp. 686-690
    • Bernado, J.M.1
  • 4
    • 0002639443 scopus 로고
    • An approach to design for generalized linear models
    • V. Fedorov and H. Läuter (Eds.), Springer, Berlin
    • Chaloner, K., An approach to design for generalized linear models, In: V. Fedorov and H. Läuter (Eds.), Model oriented data analysis, (Springer, Berlin, 1987), 3-12.
    • (1987) Model Oriented Data Analysis , pp. 3-12
    • Chaloner, K.1
  • 5
    • 0000083715 scopus 로고
    • Optimal Bayesian experimental design applied to logistic regression experiments
    • Chaloner, K., and K. Larntz, Optimal Bayesian experimental design applied to logistic regression experiments, J. Statist. Planning Inference, 21 (1989) 191-208.
    • (1989) J. Statist. Planning Inference , vol.21 , pp. 191-208
    • Chaloner, K.1    Larntz, K.2
  • 6
  • 7
    • 38249001247 scopus 로고
    • A note on optimal Bayesian design for nonlinear problems
    • Chaloner, K., A note on optimal Bayesian design for nonlinear problems, J. Stat. Planning Inference, 37 (1993) 229-236.
    • (1993) J. Stat. Planning Inference , vol.37 , pp. 229-236
    • Chaloner, K.1
  • 8
    • 0001653224 scopus 로고
    • Locally optimal designs for estimating parameters
    • Chernoff, H., Locally optimal designs for estimating parameters, Ann. Math. Statist., 24 (1953) 586-602.
    • (1953) Ann. Math. Statist. , vol.24 , pp. 586-602
    • Chernoff, H.1
  • 9
    • 0042574597 scopus 로고
    • Experimental design for a class of weighted polynomial regression models
    • Dette, H., Experimental design for a class of weighted polynomial regression models, Comput. Statist. and Data Analysis, 14 (1992) 359-373.
    • (1992) Comput. Statist. and Data Analysis , vol.14 , pp. 359-373
    • Dette, H.1
  • 11
    • 0038864482 scopus 로고
    • A note on Bayesian D-optimal designs for a generalization of the exponential growth model
    • Dette, H. and S. Sperlich, A note on Bayesian D-optimal designs for a generalization of the exponential growth model, South African Statist. J. 28 (1994) 103-118.
    • (1994) South African Statist. J. , vol.28 , pp. 103-118
    • Dette, H.1    Sperlich, S.2
  • 15
    • 0000251072 scopus 로고
    • The use of a canonical form in the construction of locally optimal designs for non-linear problems
    • C.F.J.
    • Ford, I., B. Torsney, C.F.J. and Wu . The use of a canonical form in the construction of locally optimal designs for non-linear problems, J. Roy. Statist. Soc. B, 54 (1992) 569-583.
    • (1992) J. Roy. Statist. Soc. B , vol.54 , pp. 569-583
    • Ford, I.1    Torsney, B.2    Wu3
  • 16
    • 0001097402 scopus 로고
    • s-optimal designs for multivariate polynomial regression on the q-cube
    • s-optimal designs for multivariate polynomial regression on the q-cube, Ann. Statist., 16 (1988) 1225-1240.
    • (1988) Ann. Statist. , vol.16 , pp. 1225-1240
    • Lim, Y.B.1    Studden, W.J.2
  • 17
    • 0001249987 scopus 로고
    • On a measure of information provided by an experiment
    • Lindley, D.V., On a measure of information provided by an experiment, Ann. Math. Statist., 27 (1956) 986-1005.
    • (1956) Ann. Math. Statist. , vol.27 , pp. 986-1005
    • Lindley, D.V.1
  • 18
    • 0000852422 scopus 로고
    • Bayesian D-optimal designs for the exponential growth model
    • Mukhopadhyay, S. and L. Haines, Bayesian D-optimal designs for the exponential growth model, J. Statist. Planning Inference 44 (1995) 385-398.
    • (1995) J. Statist. Planning Inference , vol.44 , pp. 385-398
    • Mukhopadhyay, S.1    Haines, L.2
  • 19
    • 0000238336 scopus 로고
    • A simplex method for function minimization
    • Nelder, J.A. and R. Mead. A simplex method for function minimization, Computer J., 7 (1965) 308-313.
    • (1965) Computer J. , vol.7 , pp. 308-313
    • Nelder, J.A.1    Mead, R.2
  • 21
    • 0022093313 scopus 로고
    • Robust experiment design via stochastic approximation
    • Pronzato, L. and E. Walter. Robust experiment design via stochastic approximation, Math. Biosc., 75, (1985) 351-356.
    • (1985) Math. Biosc. , vol.75 , pp. 351-356
    • Pronzato, L.1    Walter, E.2
  • 22
    • 84948334542 scopus 로고
    • Optimal experimental design in nonlinear regression
    • Rasch, D., Optimal experimental design in nonlinear regression, Commun. Statist. 19 (1990) 4789-4806.
    • (1990) Commun. Statist. , vol.19 , pp. 4789-4806
    • Rasch, D.1
  • 23
    • 0004202673 scopus 로고
    • American Mathematical Society, Providence, Rhode Island
    • Shohat, J.A. and J. D. Tamarkin, The problem of moments, (American Mathematical Society, Providence, Rhode Island, 1963).
    • (1963) The Problem of Moments
    • Shohat, J.A.1    Tamarkin, J.D.2
  • 25
    • 0000893312 scopus 로고
    • Extreme n-th moments for distributions on [0,1] and the inverse of a moment space map
    • Skibinsky, M., Extreme n-th moments for distributions on [0,1] and the inverse of a moment space map, J. Appl. Probab., 5 (1968) 693-701.
    • (1968) J. Appl. Probab. , vol.5 , pp. 693-701
    • Skibinsky, M.1
  • 27
    • 0000135813 scopus 로고
    • s-optimal designs for polynomial regression using continued fractions
    • s-optimal designs for polynomial regression using continued fractions, Ann. Statist., 8 (1980) 1132-1141.
    • (1980) Ann. Statist. , vol.8 , pp. 1132-1141
    • Studden, W.J.1
  • 28
    • 0000536027 scopus 로고
    • Some robust type D-optimal designs in polynomial regression
    • Studden, W.J., Some robust type D-optimal designs in polynomial regression, J. Ameri. Statist. Assoc., 77 (1982) 916-921.
    • (1982) J. Ameri. Statist. Assoc. , vol.77 , pp. 916-921
    • Studden, W.J.1
  • 30
    • 0000529562 scopus 로고
    • Some general points in the theory of optimal experimental design
    • Whittle, P., Some general points in the theory of optimal experimental design, J. Roy. Statist. Soc. Ser. B, 35 (1973) 123-130.
    • (1973) J. Roy. Statist. Soc. Ser. B , vol.35 , pp. 123-130
    • Whittle, P.1
  • 31
    • 0000558035 scopus 로고
    • Results in the theory and construction of D-optimum experimental designs
    • Wynn, H., Results in the theory and construction of D-optimum experimental designs, J. Roy. Statist. Soc. Sci. B. 34 (1972) 133-147.
    • (1972) J. Roy. Statist. Soc. Sci. B. , vol.34 , pp. 133-147
    • Wynn, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.