참고문헌
- BARRON, A. R. AND SHEU, C. H. (1991). 'Approximation of density functions by sequences of exponential families', The Annals of Statistics, 19, 1347-1369. https://doi.org/10.1214/aos/1176348252
- BERAN, R. (1979). 'Exponential models for directional data', The Annals of Statistics, 7, 1162-1178 https://doi.org/10.1214/aos/1176344838
- BIRGE, L. (1983). 'Approximation dans les espaces metriques et theorie de l'estimation', Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete, 65, 181-237 https://doi.org/10.1007/BF00532480
- BROWN, L. D. (1986). Fundamentals of Statistical Exponential Families, Institute of Mathematical Statistics, Hayward
- CHANDLER, C. AND GIBSON, A. G. (1989). 'N-body quantum scattering theory in two Hilbert spaces. V. Computation strategy', Journal of Mathematical Physics, 30, 1533-1544 https://doi.org/10.1063/1.528286
- CRAIN, B. R. (1974). 'Estimation of distributions using orthogonal expansions', The Annals of Statistics, 2, 454-463 https://doi.org/10.1214/aos/1176342706
- CRAIN, B. R. (1976a). 'Exponential models, maximum likelihood estimation, and the Haar condition', Journal of the American Statistical Association, 71, 737-740 https://doi.org/10.2307/2285612
- CRAIN, B. R. (1976b). 'More on estimation of distributions using orthogonal expansions', Journal of the American Statistical Association, 71, 741-745 https://doi.org/10.2307/2285613
- CRAIN, B. R. (1977). 'An information theoretic approach to approximating a probability distribution', SIAM Journal on Applied Mathematics, 32, 339-346 https://doi.org/10.1137/0132027
- DIACONIS, P. (1988). Group Representations in Probability and Statistics, Institute of Mathematical Statistics, Hayward
- FISHER, N. I., LEWIS, T. AND EMBLETON, B. J. (1993). Statistical Analysis of Spherical Data, Cambridge University Press, Cambridge
- GINE, E. (1975). 'Invariant tests for uniformity on compact Riemannian manifolds based on Sobolev norms', The Annals of Statistics, 3, 1243-1266 https://doi.org/10.1214/aos/1176343283
- HEALY, D. M., HENDRIKS, H. AND KIM, P. T. (1998). 'Spherical deconvolution', Journal of Multivariate Analysis, 67, 1-22 https://doi.org/10.1006/jmva.1998.1757
- HEALY, D. M. AND KIM, P. T. (1996). 'An empirical Bayes approach to directional data and efficient computation on the sphere', The Annals of Statistics, 24, 232-254 https://doi.org/10.1214/aos/1033066208
- HENDRIKS, H. (1990). 'Nonparametric estimation of a probability density on a Riemannian manifold using Fourier expansions', The Annals of Statistics, 18, 832-849 https://doi.org/10.1214/aos/1176347628
- KIM, P. T. AND Koo, J.-Y. (2000). 'Directional mixture models and optimal estimation of the mixing density', The Canadian Journal of Statistics, 28, 383-398 https://doi.org/10.2307/3315986
- Koo, J.-Y. (1993). 'Optimal rates of convergence for nonparametric statistical inverse problems', The Annals of Statistics, 21, 590-599 https://doi.org/10.1214/aos/1176349138
- Koo, J.-Y. AND CHUNG, H. Y. (1998). 'Log-density estimation in linear inverse problems', The Annals of Statistics, 26, 335-362 https://doi.org/10.1214/aos/1030563989
- Koo, J.-Y., KOOPERBERG, C. AND PARK, J. (1998). 'Logspline density estimation under censoring and truncation', Scandinavian Journal of Statistics, 26, 87-105 https://doi.org/10.1111/1467-9469.00139
- KOOPERBERG, C. AND STONE, C. J. (1991). 'A study of logspline density estimation', Computational Statistics and Data Analysis, 12, 327-347 https://doi.org/10.1016/0167-9473(91)90115-I
- KOOPERBERG, C. AND STONE, C. J. (1992). 'Logspline density estimation for censored data', Journal of Computational and Graphical Statistics, 1, 301-328 https://doi.org/10.2307/1390786
- MARDIA, K. V. AND JUPP, P. E. (2000). Directional Statistics, John Wiley & Sons, New York
- MULLER, C. (1998). Analysis of Spherical Symmetries in Euclidean Spaces, Springer-Verlag, New York
- NEYMAN, J. (1937). "'Smooth' test for goodness of fit", Scandinavian Actuarial Journal, 20, 149-199
- STONE, C. J. (1989). 'Uniform error bounds involving logspline models', In Probability, Statistics, and Mathematics: Papers in Honor of Samuel Karlin (T. W. Anderson, K. B. Athrya and D. L. Iglehart, eds.), 335-355, Academic Press, Boston
- STONE, C. J. (1990). 'Large-sample inference for logspline models', The Annals of Statistics, 18,717-741 https://doi.org/10.1214/aos/1176347622
- STONE, C. J., HANSEN, M. H., KOOPERBERG, C. AND TRUONG, Y. K. (1997) 'Polynomial splines and their tensor products in extended linear modeling (with discussion)', The Annals of Statistics, 25, 1371-1470 https://doi.org/10.1214/aos/1031594728
- STONE, C. J. AND Koo, C.-Y. (1986). 'Logspline density estimation', Contemporary Mathematics, 59, 1-15, American Mathematical Society, Providence https://doi.org/10.1090/conm/059/870445
- TAIJERON, H. J., GIBSON, A. G. AND CHANDLER, C. (1994). 'Spline interpolation and smoothing on hyperspheres', SIAM Journal on Scientific and Statistical Computing, 15, 1111-1125 https://doi.org/10.1137/0915068
- WAHBA, G. (1981). 'Spline interpolation and smoothing on the sphere', SIAM Journal on Scientific and Statistical Computing, 2, 5-16 https://doi.org/10.1137/0902002
- Xu, Y. (1997). 'Orthogonal polynomials for a family of product weight functions on the spheres', Canadian Journal of Mathematics, 49, 175-192 https://doi.org/10.4153/CJM-1997-009-4
- YATRACOS, Y. G. (1988). 'A lower bound on the error in nonparametric regression type problems', The Annals of Statistics, 16, 1180-1187 https://doi.org/10.1214/aos/1176350954