We consider the problem of determining the distribution of means of random probability measures which are obtained by normalizing increasing additive processes. A solution is found by resorting to a well-known inversion formula for characteristic functions due to Gurland. Moreover, expressions of the posterior distributions of those means, in the presence of exchangeable observations, are given. Finally, a section is devoted to the illustration of two examples of statistical relevance.
Publié le : 2003-04-14
Classification:
Dirichlet process,
distribution of means of random probability measures,
increasing addititive processes,
Lévy measure,
(normalized) random measure with independent increments,
62F15,
60G57
@article{1051027881,
author = {Regazzini, Eugenio and Lijoi, Antonio and Pr\"unster, Igor},
title = {Distributional results for means of normalized random measures with independent increments},
journal = {Ann. Statist.},
volume = {31},
number = {1},
year = {2003},
pages = { 560-585},
language = {en},
url = {http://dml.mathdoc.fr/item/1051027881}
}
Regazzini, Eugenio; Lijoi, Antonio; Prünster, Igor. Distributional results for means of normalized random measures with independent increments. Ann. Statist., Tome 31 (2003) no. 1, pp. 560-585. http://gdmltest.u-ga.fr/item/1051027881/