A widely held notion of classical conditional theory is that
statistical inference in the presence of ancillary statistics should be
independent of the distribution of those ancillary statistcs. In this paper,
ancillary paradoxes which contradict this notion are presented for two
scenarios involving confidence estimation. These results are related to
Brown’s ancillary paradox in point estimation. Moreover, the confidence
coefficient, the usual constant coverage probability estimator, is shown to be
inadmissible for confidence estimation in the multiple regression model with
random predictor variables if the dimension of the slope parameters is greater
than five. Some estimators better than the confidence coefficient are provided
in this paper. These new estimators are constructed based on empirical Bayes
estimators.
Publié le : 1999-04-14
Classification:
Confidence interval,
admissibility,
coverage function,
the usual constant coverage probability estimator,
ancillary statistic.,
62C15,
62C10
@article{1018031210,
author = {Wang, Hsiuying},
title = {Brown's paradox in the estimated confidence approach},
journal = {Ann. Statist.},
volume = {27},
number = {4},
year = {1999},
pages = { 610-626},
language = {en},
url = {http://dml.mathdoc.fr/item/1018031210}
}
Wang, Hsiuying. Brown's paradox in the estimated confidence approach. Ann. Statist., Tome 27 (1999) no. 4, pp. 610-626. http://gdmltest.u-ga.fr/item/1018031210/