The problems of estimating sequentially the intensity parameter of a homogeneous Poisson process and of estimating sequentially the mean of a sequence of i.i.d. Poisson rv's, are considered. The procedures suggested are shown to perform well for large values of the parameter and/or for small sampling cost. Having bounded regret, the procedure for estimating the mean of the Poisson sequence is asymptotically Bayes w.r.t. any sequence of a priori densities, which spread mass in a suitably smooth manner.
@article{1176344787,
author = {Vardi, Y.},
title = {Asymptotic Optimal Sequential Estimation: The Poisson Case},
journal = {Ann. Statist.},
volume = {7},
number = {1},
year = {1979},
pages = { 1040-1051},
language = {en},
url = {http://dml.mathdoc.fr/item/1176344787}
}
Vardi, Y. Asymptotic Optimal Sequential Estimation: The Poisson Case. Ann. Statist., Tome 7 (1979) no. 1, pp. 1040-1051. http://gdmltest.u-ga.fr/item/1176344787/