Multiple integral representation for functionals of Dirichlet processes

Bernoulli

Volumn 14, Issue 1, 2008, Pages 91-124

  Peccati, Giovanni ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

Bayesian statistics; Dirichlet process; Exchangeability; Hoeffding ANOVA decompositions; Jacobi polynomials; Multiple integrals; Orthogonality; U statistics; Urn sequences; Wright Fisher model

Indexed keywords

EID: 41449115541     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/07-BEJ5169     Document Type: Article

References (24)

1. Abramowitz, M. and Stegun, I.A. (1964). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards Applied Mathematics Series 55.
2. Aldous, D.J. (1983). Exchangeability and related topics. École d'Été de Probabilités de Saint-Flour XIII. Lecture Notes in Math. 1117 1-198. Berlin: Springer.
3. Blackwell, D. (1973). Discreteness of Ferguson selections. Ann. Statist. 1 356-358.
4. Blackwell, D. and MacQueen, J. (1973). Ferguson distribution via Pólya urn schemes. Ann. Statist. 1 353-355.
5. El-Dakkak, O. and Peccati, G. (2007). Hoeffding decompositions and urn sequences. Preprint.
6. Ethier, S.N. and Kurtz, T. (1986). Markov Processes: Characterization and Convergence. New York: Wiley.
7. Ethier, S.N. and Griffiths, R.C. (1993). The transition function of a Fleming-Viot process. Ann. Probab. 21 1571-1590.
8. Ferguson, T.S. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist. 1 209-230.
9. Ferguson, T.S. (1974). Prior distributions on spaces of probability measures. Ann. Statist. 2 615-629.
10. Griffiths, R.C. (1979). A transition density expansion for a multi-allele diffusion model. Adv. in Appl. Probab. 11 310-325.
11. Koroljuk, V.S. and Borovskich, Yu.V. (1994). Theory of U-Statistics. Dordrecht: Kluwer Academic Publishers.
12. Littler, R.A. and Fackerell, E.D. (1975). Transition densities for neutral multi-allele models. Biometrics 31 117-123.
13. Mauldin, R.D., Sudderth, W.D. and Williams, S.C. (1992). Pólya trees and random distributions. Ann. Statist. 20 1203-1221.
14. Nualart, D. (1995). The Malliavin Calculus and Related Topics. New York: Springer.
15. Nualart, D. and Schoutens, W. (2000). Chaotic and predictable representation for Lévy processes. Stochastic Process. Appl. 90 109-122.
16. Peccati, G. (2002). Chaos Brownien d'espace-temps, décompositions de Hoeffding et problèmes de convergence associés. Ph.D. dissertation, Univ. Paris VI.
17. Peccati, G. (2003). Hoeffding decompositions for exchangeable sequences and chaotic representation for functionals of Dirichlet processes. C. R. Math. Acad Sci. Paris 336 845-850.
18. Peccati, G. (2004). Hoeffding-ANOVA decompositions for symmetric statistics of exchangeable observations. Ann. Probab. 32 1796-1829.
19. Pitman, J. (1996). Some developments of the Blackwell-MacQueen urn scheme. In Statistics, Probability and Game Theory: Papers in Honor of David Blackwell. IMS Lecture Notes Monogr. Ser. 30. Hayward, CA: IMS.
20. James, L.F., Lijoi, A. and Prünster, I. (2006). Conjugacy as a distinctive feature of the Dirichlet process. Scand. J. Statist. 33 105-120.
21. Schleusner, J.W. (1974). A note on biorthogonal polynomials in two variables. SIAM J. Math. Anal. 5 11-18.
22. Segall, A. and Kailath, T. (1976). Orthogonal functionals of independent-increment processes. IEEE Trans. Inform. Theory 22 287-298.
23. Stroock, D.W. (1987). Homogeneous chaos revisited. Séminaire de Probabilités XXI. Lecture Notes in Math. 1247 1-8. Berlin: Springer.
24. Tsilevitch, N., Vershik, A. and Yor, M. (2001). An infinite-dimensional analogue of the Lebesgue measure and distinguished properties of the gamma process. J. Funct. Anal. 185 274-296.