Any multiresponse estimation experiment requires a decision about the number of observations to be taken. If the covariance is unknown, no fixed-sample-size procedure can guarantee that the joint confidence region will have an assigned shape and level. Double-sampling procedures use a preliminary sample of size $m$ to determine the minimum number of additional observations needed to achieve a prescribed accuracy and coverage probability for the parameter estimates. The triple-sampling procedures of this paper, less sensitive to the choice of $m$, revise the sample size estimate after collecting a fraction of the additional observations prescribed under double sampling. Second-order asymptotic results relying on conditional inference show that triple sampling is asymptotically consistent; in addition, the regret for triple sampling is a bounded function of the covariance structure and is independent of $m$.
Publié le : 1990-12-14
Classification:
Three-stage estimation,
confidence sets,
multivariate normal distribution,
sequential methods,
62H12,
62F25,
62L12
@article{1176347869,
author = {Lohr, Sharon L.},
title = {Accurate Multivariate Estimation Using Triple Sampling},
journal = {Ann. Statist.},
volume = {18},
number = {1},
year = {1990},
pages = { 1615-1633},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347869}
}
Lohr, Sharon L. Accurate Multivariate Estimation Using Triple Sampling. Ann. Statist., Tome 18 (1990) no. 1, pp. 1615-1633. http://gdmltest.u-ga.fr/item/1176347869/