메뉴 건너뛰기




Volumn 67, Issue 2, 1998, Pages 227-243

Mean Location and Sample Mean Location on Manifolds: Asymptotics, Tests, Confidence Regions

Author keywords

Mean location; degenerate normal distribution; sample Weingarten mapping; cut locus; Stiefel manifold; test; confidence interval; asymptotic; acceptance rejection method; simulation

Indexed keywords


EID: 0040678209     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1998.1776     Document Type: Article
Times cited : (64)

References (33)
  • 1
    • 0000532798 scopus 로고
    • Efficient simulation of the von Mises distribution
    • Best D. J., Fisher N. I. Efficient simulation of the von Mises distribution. Appl. Statist. 24:1979;152-157.
    • (1979) Appl. Statist. , vol.24 , pp. 152-157
    • Best, D.J.1    Fisher, N.I.2
  • 4
    • 38249018722 scopus 로고
    • The matrix angular central Gaussian distribution
    • Chikuse Y. The matrix angular central Gaussian distribution. J. Multivariate Anal. 33:1990;265-274.
    • (1990) J. Multivariate Anal. , vol.33 , pp. 265-274
    • Chikuse, Y.1
  • 5
    • 0000351907 scopus 로고
    • Orientation statistics
    • Downs T. D. Orientation statistics. Biometrika. 59:1972;665-676.
    • (1972) Biometrika , vol.59 , pp. 665-676
    • Downs, T.D.1
  • 8
    • 0011672599 scopus 로고
    • Sur le cut-locus d'une sous-variété de l'espace euclidien
    • Hendriks H. Sur le cut-locus d'une sous-variété de l'espace euclidien. C.R. Acad. Sci. Paris. Sér. I. 311:1990;637-639.
    • (1990) C.R. Acad. Sci. Paris. Sér. I , vol.311 , pp. 637-639
    • Hendriks, H.1
  • 9
    • 0000464675 scopus 로고
    • A Cramér-Rao type lower bound for estimators with values in a manifold
    • Hendriks H. A Cramér-Rao type lower bound for estimators with values in a manifold. J. Multivariate Anal. 38:1991;245-261.
    • (1991) J. Multivariate Anal. , vol.38 , pp. 245-261
    • Hendriks, H.1
  • 10
    • 0000814238 scopus 로고
    • A Cramér-Rao type inequality for random variables in Euclidean manifolds
    • Hendriks H., Janssen J., Ruymgaart F. A Cramér-Rao type inequality for random variables in Euclidean manifolds. Sankhyā-Ser. A. 54:1992;387-401.
    • (1992) Sankhyā-Ser. a , vol.54 , pp. 387-401
    • Hendriks, H.1    Janssen, J.2    Ruymgaart, F.3
  • 11
    • 0011601859 scopus 로고
    • Sur le cut-locus d'une sous-variété de l'espace euclidien. Négligeabilité
    • Hendriks H. Sur le cut-locus d'une sous-variété de l'espace euclidien. Négligeabilité C.R. Acad. Sci. Paris Sér. I. 315:1992;1275-1277.
    • (1992) C.R. Acad. Sci. Paris Sér. I , vol.315 , pp. 1275-1277
    • Hendriks, H.1
  • 12
    • 0030295988 scopus 로고    scopus 로고
    • Asymptotic behavior of sample mean direction for spheres
    • Hendriks H., Landsman Z., Ruymgaart F. Asymptotic behavior of sample mean direction for spheres. J. Multivariate Anal. 59:1996;141-152.
    • (1996) J. Multivariate Anal. , vol.59 , pp. 141-152
    • Hendriks, H.1    Landsman, Z.2    Ruymgaart, F.3
  • 13
    • 0030080006 scopus 로고    scopus 로고
    • Asymptotic behavior of sample mean location for manifolds
    • Hendriks H., Landsman Z. Asymptotic behavior of sample mean location for manifolds. Statist. Probab. Lett. 26:1996a;169-178.
    • (1996) Statist. Probab. Lett. , vol.26 , pp. 169-178
    • Hendriks, H.1    Landsman, Z.2
  • 14
    • 0039812899 scopus 로고    scopus 로고
    • Asymptotic tests for mean location on manifolds
    • Hendriks H., Landsman Z. Asymptotic tests for mean location on manifolds. C.R. Acad Sci. Paris Sér. A. 322:1996b;773-778.
    • (1996) C.R. Acad Sci. Paris Sér. a , vol.322 , pp. 773-778
    • Hendriks, H.1    Landsman, Z.2
  • 15
    • 0002416976 scopus 로고
    • Normal multivariate analysis and the orthogonal group
    • James A. T. Normal multivariate analysis and the orthogonal group. Ann. Math. Statist. 25:1954;40-75.
    • (1954) Ann. Math. Statist. , vol.25 , pp. 40-75
    • James, A.T.1
  • 17
    • 0000712295 scopus 로고
    • Maximum likelihood estimation for the matrix von Mises-Fisher and Bingham distributions
    • Jupp P. E., Mardia K. V. Maximum likelihood estimation for the matrix von Mises-Fisher and Bingham distributions. Ann. Statist. 7:1979;599-606.
    • (1979) Ann. Statist. , vol.7 , pp. 599-606
    • Jupp, P.E.1    Mardia, K.V.2
  • 18
    • 0001197510 scopus 로고
    • A unified view of the theory of directional statistics 1975-1988
    • Jupp P. E., Mardia K. V. A unified view of the theory of directional statistics 1975-1988. Internat. Statist. Rev. 57:1989;261-294.
    • (1989) Internat. Statist. Rev. , vol.57 , pp. 261-294
    • Jupp, P.E.1    Mardia, K.V.2
  • 19
    • 0002959565 scopus 로고
    • The von Mises-Fisher matrix distribution in orientation statistics
    • Khatri C. G., Mardia K. V. The von Mises-Fisher matrix distribution in orientation statistics. J. Royal Statist. Soc. B. 39:1977;95-106.
    • (1977) J. Royal Statist. Soc. B , vol.39 , pp. 95-106
    • Khatri, C.G.1    Mardia, K.V.2
  • 24
    • 0001423948 scopus 로고
    • Statistics of directional data
    • Mardia K. V. Statistics of directional data. J. Royal Statist. Soc. B. 37:1975b;349-371.
    • (1975) J. Royal Statist. Soc. B , vol.37 , pp. 349-371
    • Mardia, K.V.1
  • 25
    • 0038492192 scopus 로고
    • Uniform distribution on a Stiefel manifold
    • Mardia K. V., Khatri C. G. Uniform distribution on a Stiefel manifold. J. Multivariate Anal. 7:1977;468-473.
    • (1977) J. Multivariate Anal. , vol.7 , pp. 468-473
    • Mardia, K.V.1    Khatri, C.G.2
  • 26
    • 0011601078 scopus 로고
    • Directional data analysis: An overview
    • Mardia K. V. Directional data analysis: an overview. J. Appl. Statist. 15:1988;115-122.
    • (1988) J. Appl. Statist. , vol.15 , pp. 115-122
    • Mardia, K.V.1
  • 28
    • 0001206139 scopus 로고
    • Orientation statistics without parametric assumptions
    • Prentice M. J. Orientation statistics without parametric assumptions. J. Royal Statist. Soc. B. 48:1986;214-222.
    • (1986) J. Royal Statist. Soc. B , vol.48 , pp. 214-222
    • Prentice, M.J.1
  • 29
    • 0001263095 scopus 로고
    • Spherical regression on matched pairs of orientation statistics
    • Prentice M. J. Spherical regression on matched pairs of orientation statistics. J. Roy. Statist. Soc. B. 51:1989;241-248.
    • (1989) J. Roy. Statist. Soc. B , vol.51 , pp. 241-248
    • Prentice, M.J.1
  • 31
    • 84972497494 scopus 로고
    • Sur le cut-locus d'une variété plongée
    • Thom R. Sur le cut-locus d'une variété plongée. J. Diff. Geom. 6:1972;577-586.
    • (1972) J. Diff. Geom. , vol.6 , pp. 577-586
    • Thom, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.