An estimator $\hat{\beta}$ of $\beta$ is accurate with accuracy $A$ and confidence $\gamma, 0 < \gamma < 1,$ if $P(\hat{\beta} - \beta \in A) \geq \gamma$ for all $\beta.$ Given a sequence $Y_1, Y_2, \cdots$ of independent vector-valued homoscedastic normally-distributed random variables generated via the general linear model $Y_i = X_i\beta + \varepsilon,$ the $k$-dimensional parameter $\beta$ is accurately estimated using a sequential version of the maximum probability estimator developed by L. Weiss and J. Wolfowitz. The procedure given also generalizes C. Stein's fixed-width confidence sets to several dimensions.
Publié le : 1985-06-14
Classification:
Fixed-accuracy confidence set,
sequential methods,
nonlinear renewal theory,
general linear model,
maximum probability estimator,
62L12,
62E20,
60G40
@article{1176349546,
author = {Finster, Mark},
title = {Estimation in the General Linear Model when the Accuracy is Specified Before Data Collection},
journal = {Ann. Statist.},
volume = {13},
number = {1},
year = {1985},
pages = { 663-675},
language = {en},
url = {http://dml.mathdoc.fr/item/1176349546}
}
Finster, Mark. Estimation in the General Linear Model when the Accuracy is Specified Before Data Collection. Ann. Statist., Tome 13 (1985) no. 1, pp. 663-675. http://gdmltest.u-ga.fr/item/1176349546/