메뉴 건너뛰기




Volumn 19, Issue 2, 2013, Pages 548-598

Orthogonal polynomial kernels and canonical correlations for Dirichlet measures

Author keywords

Canonical correlations; Dirichlet distribution; Dirichlet multinomial distribution; Ewens's sampling formula; Hahn; Jacobi; Lancaster's problem; Multivariate orthogonal polynomials; Orthogonal polynomial kernels; P lya urns; Poisson Dirichlet distribution; Positive definite sequences

Indexed keywords


EID: 84884155484     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/11-BEJ403     Document Type: Article
Times cited : (22)

References (27)
  • 3
    • 0000560070 scopus 로고
    • Positive zonal functions on spheres
    • MR0068127
    • Bochner, S. (1954). Positive zonal functions on spheres. Proc. Nat. Acad. Sci. U.S.A. 40 1141-1147. MR0068127
    • (1954) Proc. Nat. Acad. Sci. U.S.A. , vol.40 , pp. 1141-1147
    • Bochner, S.1
  • 4
    • 50849137884 scopus 로고    scopus 로고
    • Gibbs sampling, exponential families and orthogonal polynomials (with comments and a rejoinder by the authors)
    • MR2446500
    • Diaconis, P., Khare, K. and Saloff-Coste, L. (2008). Gibbs sampling, exponential families and orthogonal polynomials (with comments and a rejoinder by the authors). Statist. Sci. 23 151-178. MR2446500
    • (2008) Statist. Sci. , vol.23 , pp. 151-178
    • Diaconis, P.1    Khare, K.2    Saloff-Coste, L.3
  • 6
    • 0011478689 scopus 로고
    • Polynomial expansions of bivariate distributions
    • MR0168055
    • Eagleson, G.K. (1964). Polynomial expansions of bivariate distributions. Ann. Math. Statist. 35 1208-1215. MR0168055
    • (1964) Ann. Math. Statist. , vol.35 , pp. 1208-1215
    • Eagleson, G.K.1
  • 7
    • 84980115947 scopus 로고
    • The regression system of sums with random elements in common
    • MR0226761
    • Eagleson, G.K. and Lancaster, H.O. (1967). The regression system of sums with random elements in common. Austral. J. Statist. 9 119-125. MR0226761
    • (1967) Austral. J. Statist. , vol.9 , pp. 119-125
    • Eagleson, G.K.1    Lancaster, H.O.2
  • 8
    • 0000517151 scopus 로고
    • Banach algebras for Jacobi series and positivity of a kernel
    • MR0310536
    • Gasper, G. (1972). Banach algebras for Jacobi series and positivity of a kernel. Ann. of Math. (2) 95 261-280. MR0310536
    • (1972) Ann. of Math. , vol.2 , Issue.95 , pp. 261-280
    • Gasper, G.1
  • 9
    • 0000491534 scopus 로고
    • Nonnegativity of a discrete Poisson kernel for the Hahn polynomials
    • Collection of articles dedicated to Salomon Bochner. MR0320392
    • Gasper, G. (1973). Nonnegativity of a discrete Poisson kernel for the Hahn polynomials. J. Math. Anal. Appl. 42 438-451. Collection of articles dedicated to Salomon Bochner. MR0320392
    • (1973) J. Math. Anal. Appl. , vol.42 , pp. 438-451
    • Gasper, G.1
  • 10
    • 0041532932 scopus 로고
    • On the distribution of allele frequencies in a diffusion model
    • MR0528914
    • Griffiths, R.C. (1979). On the distribution of allele frequencies in a diffusion model. Theoret. Population Biol. 15 140-158. MR0528914
    • (1979) Theoret. Population Biol. , vol.15 , pp. 140-158
    • Griffiths, R.C.1
  • 11
    • 0002615334 scopus 로고
    • A transition density expansion for a multi-allele diffusion model
    • MR0526415
    • Griffiths, R.C. (1979). A transition density expansion for a multi-allele diffusion model. Adv. in Appl. Probab. 11 310-325. MR0526415
    • (1979) Adv. in Appl. Probab. , vol.11 , pp. 310-325
    • Griffiths, R.C.1
  • 12
    • 0018980316 scopus 로고
    • Lines of descent in the diffusion approximation of neutral Wright-Fisher models
    • MR0568666
    • Griffiths, R.C. (1980). Lines of descent in the diffusion approximation of neutral Wright-Fisher models. Theoret. Population Biol. 17 37-50. MR0568666
    • (1980) Theoret. Population Biol. , vol.17 , pp. 37-50
    • Griffiths, R.C.1
  • 13
    • 33745955125 scopus 로고    scopus 로고
    • Coalescent lineage distributions
    • MR2264950
    • Griffiths, R.C. (2006). Coalescent lineage distributions. Adv. in Appl. Probab. 38 405-429. MR2264950
    • (2006) Adv. in Appl. Probab. , vol.38 , pp. 405-429
    • Griffiths, R.C.1
  • 15
    • 79960237408 scopus 로고    scopus 로고
    • Multivariate Jacobi and Laguerre polynomials, infinitedimensional extensions, and their probabilistic connections with multivariate Hahn and Meixner polynomials
    • Griffiths, R.C. and Spanò, D. (2011). Multivariate Jacobi and Laguerre polynomials, infinitedimensional extensions, and their probabilistic connections with multivariate Hahn and Meixner polynomials. Bernoulli 17 1095-1125.
    • (2011) Bernoulli , vol.17 , pp. 1095-1125
    • Griffiths, R.C.1    Spanò, D.2
  • 18
    • 66149104541 scopus 로고    scopus 로고
    • Rates of convergence of some multivariate Markov chains with polynomial eigenfunctions
    • MR2521887
    • Khare, K. and Zhou, H. (2009). Rates of convergence of some multivariate Markov chains with polynomial eigenfunctions. Ann. Appl. Probab. 19 737-777. MR2521887
    • (2009) Ann. Appl. Probab. , vol.19 , pp. 737-777
    • Khare, K.1    Zhou, H.2
  • 19
    • 0002453994 scopus 로고
    • Random discrete distribution
    • With a discussion by S.J. Taylor, A.G. Hawkes, A.M.Walker, D.R. Cox, A.F.M. Smith, B.M. Hill, P.J. Burville, T. Leonard and a reply by the author. MR0368264
    • Kingman, J.F.C., Taylor, S.J., Hawkes, A.G., Walker, A.M., Cox, D.R., Smith, A.F.M., Hill, B.M., Burville, P.J. and Leonard, T. (1975). Random discrete distribution. J. Roy. Statist. Soc. Ser. B 37 1- 22.With a discussion by S.J. Taylor, A.G. Hawkes, A.M.Walker, D.R. Cox, A.F.M. Smith, B.M. Hill, P.J. Burville, T. Leonard and a reply by the author. MR0368264
    • (1975) J. Roy. Statist. Soc. Ser. B , vol.37 , pp. 1-22
    • Kingman, J.F.C.1    Taylor, S.J.2    Hawkes, A.G.3    Walker, A.M.4    Cox, D.R.5    Smith, A.F.M.6    Hill, B.M.7    Burville, P.J.8    Leonard, T.9
  • 20
    • 0000886086 scopus 로고
    • Jacobi polynomials. II. An analytic proof of the product formula
    • MR0385198
    • Koornwinder, T. (1974). Jacobi polynomials. II. An analytic proof of the product formula. SIAM J. Math. Anal. 5 125-137. MR0385198
    • (1974) SIAM J. Math. Anal. , vol.5 , pp. 125-137
    • Koornwinder, T.1
  • 21
    • 0031485010 scopus 로고    scopus 로고
    • Product formulas and associated hypergroups for orthogonal polynomials on the simplex and on a parabolic biangle
    • MR1466065
    • Koornwinder, T.H. and Schwartz, A.L. (1997). Product formulas and associated hypergroups for orthogonal polynomials on the simplex and on a parabolic biangle. Constr. Approx. 13 537-567. MR1466065
    • (1997) Constr. Approx. , vol.13 , pp. 537-567
    • Koornwinder, T.H.1    Schwartz, A.L.2
  • 22
    • 0001028404 scopus 로고
    • The structure of bivariate distributions
    • MR0102150
    • Lancaster, H.O. (1958). The structure of bivariate distributions. Ann. Math. Statist. 29 719-736. MR0102150
    • (1958) Ann. Math. Statist. , vol.29 , pp. 719-736
    • Lancaster, H.O.1
  • 23
    • 14844351003 scopus 로고    scopus 로고
    • Partially exchangeable processes indexed by the vertices of a k-tree constructed via reinforcement
    • MR2128635
    • Muliere, P., Secchi, P. andWalker, S. (2005). Partially exchangeable processes indexed by the vertices of a k-tree constructed via reinforcement. Stochastic Process. Appl. 115 661-677. MR2128635
    • (2005) Stochastic Process. Appl. , vol.115 , pp. 661-677
    • Muliere, P.1    Secchi, P.2    Walker, S.3
  • 24
    • 41449115541 scopus 로고    scopus 로고
    • Multiple integral representation for functionals of Dirichlet processes
    • MR2401655
    • Peccati, G. (2008). Multiple integral representation for functionals of Dirichlet processes. Bernoulli 14 91-124. MR2401655
    • (2008) Bernoulli , vol.14 , pp. 91-124
    • Peccati, G.1
  • 25
    • 0032622621 scopus 로고    scopus 로고
    • Multivariable orthogonal polynomials and coupling coefficients for discrete series representations
    • (electronic). MR1664759
    • Rosengren, H. (1999). Multivariable orthogonal polynomials and coupling coefficients for discrete series representations. SIAM J. Math. Anal. 30 232-272 (electronic). MR1664759
    • (1999) SIAM J. Math. Anal. , vol.30 , pp. 232-272
    • Rosengren, H.1
  • 26
    • 33646355419 scopus 로고    scopus 로고
    • On the Bernstein-Bézier form of Jacobi polynomials on a simplex
    • MR2226679
    • Waldron, S. (2006). On the Bernstein-Bézier form of Jacobi polynomials on a simplex. J. Approx. Theory 140 86-99. MR2226679
    • (2006) J. Approx. Theory , vol.140 , pp. 86-99
    • Waldron, S.1
  • 27
    • 0001769846 scopus 로고
    • Lines of descent and the coalescent
    • MR0760232
    • Watterson, G.A. (1984). Lines of descent and the coalescent. Theoret. Population Biol. 26 77-92. MR0760232
    • (1984) Theoret. Population Biol. , vol.26 , pp. 77-92
    • Watterson, G.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.