The problem of designing an experiment to estimate the difference between the means of two normal populations with unit variances is considered, when the cost of drawing a sample from either population may depend on unknown parameters. A quasi-Bayesian approach is adopted in which the mean difference is estimated by its maximum likelihood estimator, but the design (allocation rule) is evaluated in Bayesian, decision-theoretic terms. A three-stage procedure is proposed and its risk evaluated, up to terms which are small compared to the cost of a single observation. This procedure is shown to be optimal to second order for squared error loss.
Publié le : 1990-09-14
Classification:
Loss function,
sampling costs,
integrated risk,
invariance,
sequential designs,
posterior distributions,
asymptotic normality,
62L12
@article{1176347754,
author = {Woodroofe, Michael and Hardwick, Janis},
title = {Sequential Allocation for an Estimation Problem with Ethical Costs},
journal = {Ann. Statist.},
volume = {18},
number = {1},
year = {1990},
pages = { 1358-1377},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347754}
}
Woodroofe, Michael; Hardwick, Janis. Sequential Allocation for an Estimation Problem with Ethical Costs. Ann. Statist., Tome 18 (1990) no. 1, pp. 1358-1377. http://gdmltest.u-ga.fr/item/1176347754/