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Volumn 29, Issue 4, 2001, Pages 1024-1049

Robust designs for polynomial regression by maximizing a minimum of D-and D1-efficiencies

Author keywords

Associated orthogonal polynomials; D optimality; D1 optimality; Minimax optimal designs; Robust design; T test

Indexed keywords


EID: 0035732070     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1013699990     Document Type: Article
Times cited : (24)

References (32)
  • 2
    • 84909574881 scopus 로고
    • A basis for the selection of a response surface design
    • BOX, G. E. P. and DRAPER, N. R. (1959). A basis for the selection of a response surface design. J. Amer. Statist. Assoc. 54 622-654.
    • (1959) J. Amer. Statist. Assoc. , vol.54 , pp. 622-654
    • Box, G.E.P.1    Draper, N.R.2
  • 4
    • 0001125645 scopus 로고
    • 1-optimal design in polynomial regression
    • 1-optimal design in polynomial regression. Ann. Statist. 18 1784-1804.
    • (1990) Ann. Statist. , vol.18 , pp. 1784-1804
    • Dette, H.1
  • 5
    • 21844516944 scopus 로고
    • Optimal designs for identifying the degree of a polynomial regression
    • DETTE, H. (1995). Optimal designs for identifying the degree of a polynomial regression. Ann. Statist. 23 1248-1266.
    • (1995) Ann. Statist. , vol.23 , pp. 1248-1266
    • Dette, H.1
  • 8
    • 0022809862 scopus 로고
    • The weight functions, generating functions and miscellaneous properties of the sequences of orthogonal polynomials of the second kind associated with the Jacobi and the Gegenbauer polynomials
    • GROSJEAN, C. C. (1986). The weight functions, generating functions and miscellaneous properties of the sequences of orthogonal polynomials of the second kind associated with the Jacobi and the Gegenbauer polynomials. J. Comp. Appl. Math. 18 259-307.
    • (1986) J. Comp. Appl. Math. , vol.18 , pp. 259-307
    • Grosjean, C.C.1
  • 9
    • 0001744030 scopus 로고
    • The spacing of observations in polynomial regression
    • GUEST, P. G. (1958). The spacing of observations in polynomial regression. Ann. Math. Statist. 29 294-299.
    • (1958) Ann. Math. Statist. , vol.29 , pp. 294-299
    • Guest, P.G.1
  • 10
    • 0001619680 scopus 로고
    • Efficiency problems in polynomial estimation
    • HOEL, P. G. (1958). Efficiency problems in polynomial estimation. Ann. Math. Statist. 29 1134-1145.
    • (1958) Ann. Math. Statist. , vol.29 , pp. 1134-1145
    • Hoel, P.G.1
  • 11
    • 0002334709 scopus 로고
    • Robustness and designs
    • J. N. Srivastava, ed. North Holland, Amsterdam
    • HUBER, P. J. (1975). Robustness and designs. In A Survey of Statistical Designs (J. N. Srivastava, ed.) 287-301. North Holland, Amsterdam.
    • (1975) A Survey of Statistical Designs , pp. 287-301
    • Huber, P.J.1
  • 12
    • 0000981128 scopus 로고
    • General equivalence theory for optimum designs (approximate theory)
    • KIEFER, J. C. (1974). General equivalence theory for optimum designs (approximate theory). Ann. Statist. 2 849-879.
    • (1974) Ann. Statist. , vol.2 , pp. 849-879
    • Kiefer, J.C.1
  • 13
    • 0000448225 scopus 로고
    • Optimum designs in regression problems
    • KIEFER, J. C. and WOLFOWITZ, J. (1959). Optimum designs in regression problems. Ann. Math. Statist. 30 271-294.
    • (1959) Ann. Math. Statist. , vol.30 , pp. 271-294
    • Kiefer, J.C.1    Wolfowitz, J.2
  • 14
    • 84966244168 scopus 로고
    • Orthogonal polynomials and hypergroups II: The symmetric case
    • LASSER, R. (1994). Orthogonal polynomials and hypergroups II: the symmetric case. Trans. Amer. Math. Soc. 341 749-770.
    • (1994) Trans. Amer. Math. Soc. , vol.341 , pp. 749-770
    • Lasser, R.1
  • 16
    • 0003141877 scopus 로고
    • D-optimal designs on the unit q-ball
    • LAU, T. S. (1988). D-optimal designs on the unit q-ball. J. Statist. Plann. Inference 19 299-315.
    • (1988) J. Statist. Plann. Inference , vol.19 , pp. 299-315
    • Lau, T.S.1
  • 17
    • 0000965352 scopus 로고
    • Experimental design in a class of models
    • LÄUTER, E. (1974). Experimental design in a class of models. Math. Oper. Statist. 5 379-398.
    • (1974) Math. Oper. Statist. , vol.5 , pp. 379-398
    • Läuter, E.1
  • 19
    • 21144471847 scopus 로고
    • E-optimal designs for polynomial regression
    • PUKELSHEIM, F. and STUDDEN, W. J. (1993). E-optimal designs for polynomial regression. Ann. Statist. 21 402-415.
    • (1993) Ann. Statist. , vol.21 , pp. 402-415
    • Pukelsheim, F.1    Studden, W.J.2
  • 20
  • 21
    • 0000819909 scopus 로고
    • The range of the (n + 1)th moment for distributions on [0, 1]
    • SKIBINSKY, M. (1967). The range of the (n + 1)th moment for distributions on [0, 1]. J. Appl. Probab. 4 543-552.
    • (1967) J. Appl. Probab. , vol.4 , pp. 543-552
    • Skibinsky, M.1
  • 22
    • 38249040783 scopus 로고
    • Principal representations and canonical moment sequences for distributions on an interval
    • SKIBINSKY, M. (1986). Principal representations and canonical moment sequences for distributions on an interval. J. Math. Anal. Appl. 120 95-120.
    • (1986) J. Math. Anal. Appl. , vol.120 , pp. 95-120
    • Skibinsky, M.1
  • 23
    • 0039608905 scopus 로고
    • Good designs for testing the degree of a polynomial mean
    • SPRUILL, M. G. (1990). Good designs for testing the degree of a polynomial mean. Sankhyā Ser. B 52 67-74.
    • (1990) Sankhyā Ser. B , vol.52 , pp. 67-74
    • Spruill, M.G.1
  • 24
    • 84948260204 scopus 로고
    • Optimal experimental design for polynomial regression
    • STIGLER, S. (1971). Optimal experimental design for polynomial regression. J. Amer. Statist. Assoc. 66 311-318.
    • (1971) J. Amer. Statist. Assoc. , vol.66 , pp. 311-318
    • Stigler, S.1
  • 25
    • 0001461163 scopus 로고
    • Optimal designs on Tchebycheff points
    • STUDDEN, W. J. (1968). Optimal designs on Tchebycheff points. Ann. Math. Statist. 39 1435-1447.
    • (1968) Ann. Math. Statist. , vol.39 , pp. 1435-1447
    • Studden, W.J.1
  • 26
    • 0000135813 scopus 로고
    • s-optimal designs for polynomial regression using continued fractions
    • s-optimal designs for polynomial regression using continued fractions. Ann. Statist. 8 1132-1141.
    • (1980) Ann. Statist. , vol.8 , pp. 1132-1141
    • Studden, W.J.1
  • 27
    • 0000685915 scopus 로고
    • Optimal designs for weighted polynomial regression using canonical moments
    • S. S. Gupta and J. O. Berger, eds. Academic Press, New York
    • STUDDEN, W. J. (1982a). Optimal designs for weighted polynomial regression using canonical moments. In Statistical Decision Theory and Related Topics III 2 (S. S. Gupta and J. O. Berger, eds.) 335-350. Academic Press, New York.
    • (1982) Statistical Decision Theory and Related Topics III , vol.2 , pp. 335-350
    • Studden, W.J.1
  • 28
    • 0000536027 scopus 로고
    • Some robust-type D-optimal designs in polynomial regression
    • STUDDEN, W. J. (1982b). Some robust-type D-optimal designs in polynomial regression. J. Amer. Statist. Assoc. 77 916-921.
    • (1982) J. Amer. Statist. Assoc. , vol.77 , pp. 916-921
    • Studden, W.J.1
  • 29
    • 0002313503 scopus 로고
    • p-optimal designs for polynomial regression
    • p-optimal designs for polynomial regression. Ann. Statist. 17 618-623.
    • (1989) Ann. Statist. , vol.17 , pp. 618-623
    • Studden, W.J.1
  • 30
    • 0040905491 scopus 로고
    • Amer. Math. Soc. Colloq. Publ., Providence, RI
    • SZEGÖ, G. (1975). Orthogonal Polynomials. Amer. Math. Soc. Colloq. Publ., Providence, RI.
    • (1975) Orthogonal Polynomials
    • Szegö, G.1
  • 31
    • 0002357830 scopus 로고
    • Minimax designs for approximately linear regression
    • WIENS, D. P. (1992). Minimax designs for approximately linear regression. J. Statist. Plann. Inference 31 353-371.
    • (1992) J. Statist. Plann. Inference , vol.31 , pp. 353-371
    • Wiens, D.P.1
  • 32
    • 0039127251 scopus 로고
    • Comparing robust properties of A-, D-, E-and G-optimal designs
    • WONG, W. K. (1994). Comparing robust properties of A-, D-, E-and G-optimal designs. Comput. Statist. Data Anal. 18 441-448.
    • (1994) Comput. Statist. Data Anal. , vol.18 , pp. 441-448
    • Wong, W.K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.