메뉴 건너뛰기




Volumn 99, Issue 3, 2008, Pages 465-489

An implicit function approach to constrained optimization with applications to asymptotic expansions

Author keywords

Bordered determinantal criterion; Bordered Hessian; Edgeworth expansions; Estimating functions; Factor analysis; Lagrange multipliers; Matrix derivatives; Second derivative test; Singular value decomposition; Taylor series expansions

Indexed keywords


EID: 38349108749     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2007.01.005     Document Type: Article
Times cited : (9)

References (33)
  • 1
    • 0001091851 scopus 로고
    • Maximum-likelihood estimation of parameters subject to restraints
    • Aitchison J., and Silvey S.D. Maximum-likelihood estimation of parameters subject to restraints. Ann. Math. Statist. 29 (1958) 813-828
    • (1958) Ann. Math. Statist. , vol.29 , pp. 813-828
    • Aitchison, J.1    Silvey, S.D.2
  • 2
    • 0001397884 scopus 로고
    • Standard errors for rotated factor loadings
    • Archer C.O., and Jennrich R.I. Standard errors for rotated factor loadings. Psychometrika 38 (1973) 581-592
    • (1973) Psychometrika , vol.38 , pp. 581-592
    • Archer, C.O.1    Jennrich, R.I.2
  • 3
    • 23844500141 scopus 로고    scopus 로고
    • Second-order accurate inference on eigenvalues of covariance and correlation matrices
    • Boik R.J. Second-order accurate inference on eigenvalues of covariance and correlation matrices. J. Multivariate Anal. 96 (2005) 136-171
    • (2005) J. Multivariate Anal. , vol.96 , pp. 136-171
    • Boik, R.J.1
  • 4
    • 38349085742 scopus 로고    scopus 로고
    • R.J. Boik, Newton algorithms for analytic rotation: an implicit function approach, Technical Report #9-12-06, Department of Mathematical Sciences, Montana State University, Bozeman, MT.
  • 5
    • 85004809746 scopus 로고
    • Gradient methods for analytic rotation
    • Browne M.W. Gradient methods for analytic rotation. British J. Math. Statist. Psych. 27 (1974) 115-121
    • (1974) British J. Math. Statist. Psych. , vol.27 , pp. 115-121
    • Browne, M.W.1
  • 6
    • 0003159680 scopus 로고
    • Quartic rotation criteria and algorithms
    • Clarkson D.B., and Jennrich R.I. Quartic rotation criteria and algorithms. Psychometrika 53 (1988) 251-259
    • (1988) Psychometrika , vol.53 , pp. 251-259
    • Clarkson, D.B.1    Jennrich, R.I.2
  • 7
    • 0002619220 scopus 로고
    • Factor analysis by Lawley's method of maximum likelihood
    • Emmett W.G. Factor analysis by Lawley's method of maximum likelihood. British J. Psych. Statist. Sec. 2 (1949) 90-97
    • (1949) British J. Psych. Statist. Sec. , vol.2 , pp. 90-97
    • Emmett, W.G.1
  • 11
    • 38349159711 scopus 로고    scopus 로고
    • Estimating functions: A synthesis of least squares and maximum likelihood methods
    • Basawa I.V., Godambe V.P., and Taylor R.L. (Eds), Institute of Mathematical Statistics, Hayward CA
    • Godambe V.P. Estimating functions: A synthesis of least squares and maximum likelihood methods. In: Basawa I.V., Godambe V.P., and Taylor R.L. (Eds). Selected Proceedings of the Symposium on Estimating Functions (1997), Institute of Mathematical Statistics, Hayward CA 5-15
    • (1997) Selected Proceedings of the Symposium on Estimating Functions , pp. 5-15
    • Godambe, V.P.1
  • 14
    • 38349188325 scopus 로고    scopus 로고
    • Hessian sufficiency for bordered Hessian
    • Im E.K. Hessian sufficiency for bordered Hessian. Res. Lett. Inf. Math. Sci. 8 (2005) 189-196
    • (2005) Res. Lett. Inf. Math. Sci. , vol.8 , pp. 189-196
    • Im, E.K.1
  • 15
    • 0001397883 scopus 로고
    • Standard errors for obliquely rotated factor loadings
    • Jennrich R.I. Standard errors for obliquely rotated factor loadings. Psychometrika 38 (1973) 593-604
    • (1973) Psychometrika , vol.38 , pp. 593-604
    • Jennrich, R.I.1
  • 16
    • 85004766168 scopus 로고
    • Simplified formulae for standard errors in maximum likelihood factor analysis
    • Jennrich R.I. Simplified formulae for standard errors in maximum likelihood factor analysis. British J. Math. Statist. Psych. 27 (1974) 122-131
    • (1974) British J. Math. Statist. Psych. , vol.27 , pp. 122-131
    • Jennrich, R.I.1
  • 17
    • 34250922831 scopus 로고
    • The varimax criterion for analytic rotation in factor analysis
    • Kaiser H.F. The varimax criterion for analytic rotation in factor analysis. Psychometrika 23 (1958) 187-200
    • (1958) Psychometrika , vol.23 , pp. 187-200
    • Kaiser, H.F.1
  • 18
    • 0002758064 scopus 로고
    • A note on a MANOVA model applied to problems in growth curve
    • Khatri C.G. A note on a MANOVA model applied to problems in growth curve. Ann. Inst. Statist. Math. 18 (1966) 75-86
    • (1966) Ann. Inst. Statist. Math. , vol.18 , pp. 75-86
    • Khatri, C.G.1
  • 20
    • 0000387723 scopus 로고
    • Matrix derivatives with an application to an adaptive linear decision problem
    • MacRae E.C. Matrix derivatives with an application to an adaptive linear decision problem. Ann. Statist. 2 (1974) 337-346
    • (1974) Ann. Statist. , vol.2 , pp. 337-346
    • MacRae, E.C.1
  • 22
    • 84988119518 scopus 로고
    • Some results on commutation matrices with statistical applications
    • Neudecker H., and Wansbeek T. Some results on commutation matrices with statistical applications. Canad. J. Statist. 11 (1983) 221-231
    • (1983) Canad. J. Statist. , vol.11 , pp. 221-231
    • Neudecker, H.1    Wansbeek, T.2
  • 24
    • 0009968549 scopus 로고    scopus 로고
    • On the standard errors of rotated factor loadings with weights for observed variables
    • Ogasawara H. On the standard errors of rotated factor loadings with weights for observed variables. Behaviormetrika 27 (2000) 1-14
    • (2000) Behaviormetrika , vol.27 , pp. 1-14
    • Ogasawara, H.1
  • 25
    • 38349187033 scopus 로고    scopus 로고
    • H. Ogasawara, Asymptotic expansion in factor analysis and structural equation modeling under nonnormality/normality, Paper presented at the 72nd annual meeting of Japan Statistical Society, Fuji University, Hanamaki, Japan, 2004.
  • 26
    • 84989446443 scopus 로고
    • Estimating equations, empirical likelihood and constraints on parameters
    • Qin J., and Lawless J. Estimating equations, empirical likelihood and constraints on parameters. Canad. J. Statist. 23 (1995) 145-159
    • (1995) Canad. J. Statist. , vol.23 , pp. 145-159
    • Qin, J.1    Lawless, J.2
  • 27
    • 84966240253 scopus 로고
    • On direct product matrices
    • Roth W.E. On direct product matrices. Bull. Amer. Math. Soc. 40 (1934) 461-468
    • (1934) Bull. Amer. Math. Soc. , vol.40 , pp. 461-468
    • Roth, W.E.1
  • 29
    • 0001652862 scopus 로고
    • The Lagrangian multiplier test
    • Silvey S.D. The Lagrangian multiplier test. Ann. Math. Statist. 30 (1959) 389-407
    • (1959) Ann. Math. Statist. , vol.30 , pp. 389-407
    • Silvey, S.D.1
  • 31
    • 3743065438 scopus 로고
    • Multivariate maxima and minima with matrix derivatives
    • Tracy D.S., and Dwyer P.S. Multivariate maxima and minima with matrix derivatives. J. Amer. Statist. Assoc. 64 (1969) 1576-1594
    • (1969) J. Amer. Statist. Assoc. , vol.64 , pp. 1576-1594
    • Tracy, D.S.1    Dwyer, P.S.2
  • 32
    • 0001040805 scopus 로고    scopus 로고
    • Asymptotics of estimating equations under natural conditions
    • Yuan K.-H., and Jennrich R.I. Asymptotics of estimating equations under natural conditions. J. Multivariate. Anal. 65 (1998) 245-260
    • (1998) J. Multivariate. Anal. , vol.65 , pp. 245-260
    • Yuan, K.-H.1    Jennrich, R.I.2
  • 33
    • 6744262250 scopus 로고    scopus 로고
    • Estimating equations with nuisance parameters: theory and application
    • Yuan K.-H., and Jennrich R.I. Estimating equations with nuisance parameters: theory and application. Ann. Inst. Statist. Math. 52 (2000) 343-350
    • (2000) Ann. Inst. Statist. Math. , vol.52 , pp. 343-350
    • Yuan, K.-H.1    Jennrich, R.I.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.