This paper considers the problem of sequentially estimating the mean of a normal distribution when the variance is unknown. A continuous time analogue of the discrete time problem is studied. For $L$ in a class of loss functions, properties of the value function and optimal continuation region of $L$ are presented. Asymptotic expansions are found for the value function and the optimal boundary function of the loss function $L$.
Publié le : 1980-11-14
Classification:
Bayesian sequential estimation,
normal distribution,
gamma distribution,
normal-gamma prior distribution,
loss function,
value function,
optimal continuation region,
optimal stopping rule,
asymptotic approximations,
62L12,
62F10,
62L15,
60J25,
60J30,
62F15
@article{1176345196,
author = {Rasmussen, Shelley L.},
title = {A Bayesian Approach to a Problem in Sequential Estimation},
journal = {Ann. Statist.},
volume = {8},
number = {1},
year = {1980},
pages = { 1229-1243},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345196}
}
Rasmussen, Shelley L. A Bayesian Approach to a Problem in Sequential Estimation. Ann. Statist., Tome 8 (1980) no. 1, pp. 1229-1243. http://gdmltest.u-ga.fr/item/1176345196/