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Volumn 28, Issue 2, 2000, Pages 383-398

Directional mixture models and optimal estimation of the mixing density

Author keywords

Addition formula; Fano's lemma; Gaussian distribution; Laplace distribution; Smoothness conditions; Spherical harmonics; Von mises fisher distribution

Indexed keywords


EID: 0034343794     PISSN: 03195724     EISSN: None     Source Type: Journal    
DOI: 10.2307/3315986     Document Type: Article
Times cited : (14)

References (27)
  • 2
    • 38249026793 scopus 로고
    • Kernel estimators of density function of directional data
    • Z. D. Bai, C. R. Rao & L. C. Zhao (1988). Kernel estimators of density function of directional data. Journal of Multivariate Analysis, 27, 24-39.
    • (1988) Journal of Multivariate Analysis , vol.27 , pp. 24-39
    • Bai, Z.D.1    Rao, C.R.2    Zhao, L.C.3
  • 3
    • 0000121741 scopus 로고
    • Exponential models for directional data
    • R. Beran (1979). Exponential models for directional data. The Annals of Statistics, 6, 1162-1178.
    • (1979) The Annals of Statistics , vol.6 , pp. 1162-1178
    • Beran, R.1
  • 6
    • 0000273884 scopus 로고
    • Computing Fourier transforms and convolutions on the 2-sphere
    • J. R. Driscoll & D. M. Healy Jr (1994). Computing Fourier transforms and convolutions on the 2-sphere. Advances in Applied Mathematics, 15, 202-250.
    • (1994) Advances in Applied Mathematics , vol.15 , pp. 202-250
    • Driscoll, J.R.1    Healy D.M., Jr.2
  • 7
    • 0000867838 scopus 로고
    • On the optimal rates of convergence for nonparametric deconvolution problems
    • J. Fan (1991). On the optimal rates of convergence for nonparametric deconvolution problems. The Annals of Statistics, 19, 1257-1272.
    • (1991) The Annals of Statistics , vol.19 , pp. 1257-1272
    • Fan, J.1
  • 9
    • 0000861689 scopus 로고
    • Invariant tests for uniformity on compact Riemannian manifolds based on Sobolev norms
    • E. Giné (1975). Invariant tests for uniformity on compact Riemannian manifolds based on Sobolev norms. The Annals of Statistics, 6, 1243-1266.
    • (1975) The Annals of Statistics , vol.6 , pp. 1243-1266
    • Giné, E.1
  • 11
    • 0001445530 scopus 로고
    • Kernel density estimation with spherical data
    • P. Hall, G. Watson & J. Cabrera (1987). Kernel density estimation with spherical data. Biometrika, 74, 751-762.
    • (1987) Biometrika , vol.74 , pp. 751-762
    • Hall, P.1    Watson, G.2    Cabrera, J.3
  • 12
    • 0001557950 scopus 로고
    • "Normal" distribution functions on spheres and the modified Bessel functions
    • P. Hartman & G. Watson (1974). "Normal" distribution functions on spheres and the modified Bessel functions. The Annals of Probability, 2, 593-607.
    • (1974) The Annals of Probability , vol.2 , pp. 593-607
    • Hartman, P.1    Watson, G.2
  • 14
    • 0030543857 scopus 로고    scopus 로고
    • An empirical Bayes approach to directional data and efficient computation on the sphere
    • D. M. Healy Jr & P. T. Kim (1996). An empirical Bayes approach to directional data and efficient computation on the sphere. The Annals of Statistics, 24, 232-254.
    • (1996) The Annals of Statistics , vol.24 , pp. 232-254
    • Healy D.M., Jr.1    Kim, P.T.2
  • 15
    • 0001583657 scopus 로고
    • Nonparametric estimation of a probability density on a Riemannian manifold using Fourier expansions
    • H. Hendriks (1990). Nonparametric estimation of a probability density on a Riemannian manifold using Fourier expansions. The Annals of Statistics, 18, 832-849.
    • (1990) The Annals of Statistics , vol.18 , pp. 832-849
    • Hendriks, H.1
  • 16
    • 21144470411 scopus 로고
    • Optimal rates of convergence for nonparametric statistical inverse problems
    • J. Y. Koo (1993). Optimal rates of convergence for nonparametric statistical inverse problems. The Annals of Statistics, 21, 590-599.
    • (1993) The Annals of Statistics , vol.21 , pp. 590-599
    • Koo, J.Y.1
  • 17
    • 0032373643 scopus 로고    scopus 로고
    • Log-density estimation in linear inverse problems
    • J. Y. Koo & H. Y. Chung (1998). Log-density estimation in linear inverse problems. The Annals of Statistics, 26, 335-362.
    • (1998) The Annals of Statistics , vol.26 , pp. 335-362
    • Koo, J.Y.1    Chung, H.Y.2
  • 21
    • 0000439528 scopus 로고
    • Optimal rates of convergence for nonparametric estimators
    • C. J. Stone (1980). Optimal rates of convergence for nonparametric estimators. The Annals of Statistics, 8, 1348-1360.
    • (1980) The Annals of Statistics , vol.8 , pp. 1348-1360
    • Stone, C.J.1
  • 26
    • 0001748155 scopus 로고
    • A lower bound on the error in nonparametric regression type problems
    • Y. G. Yatracos (1988). A lower bound on the error in nonparametric regression type problems. The Annals of Statistics, 16, 1180-1187.
    • (1988) The Annals of Statistics , vol.16 , pp. 1180-1187
    • Yatracos, Y.G.1
  • 27
    • 0002055609 scopus 로고
    • Fourier methods for estimating mixing densities and distributions
    • C. H. Zhang (1990). Fourier methods for estimating mixing densities and distributions. The Annals of Statistics, 18, 806-831.
    • (1990) The Annals of Statistics , vol.18 , pp. 806-831
    • Zhang, C.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.