A pretest procedure consists of a preliminary test on a nuisance
parameter, investigating whether it equals a given value or not, followed by
the main testing problem on the parameter of interest. In case of acceptance of
the preliminary test, the main test is applied in the restricted family with
the given value of the nuisance parameter, while otherwise the test is
performed in the complete family, including the nuisance parameter. For an
appropriate class of tests, containing all standard first-order optimal tests,
an attractive expression for the difference in size and power between the
pretest procedure and the test in the complete family is derived using
second-order asymptotics. For a very great part the result is the same for all
members of the class. From this expression considerable insight can be obtained
in a qualitative and quantitative sense. The results can be applied easily as
is illustrated by a number of practical examples, where also the accuracy of
the approximations is seen from comparison with numerical results.
Publié le : 2000-02-14
Classification:
Pretest procedure,
second-order asymptotics,
locally most powerful test,
likelihood ratio test,
Rao’s test,
Wald’s test,
two-parameter exponential families,
location- scale families,
62F05,
62E20
@article{1016120369,
author = {Albers, Willem and Boon, Pieta C. and Kallenberg, Wilbert C. M.},
title = {Size and power of pretest procedures},
journal = {Ann. Statist.},
volume = {28},
number = {3},
year = {2000},
pages = { 195-214},
language = {en},
url = {http://dml.mathdoc.fr/item/1016120369}
}
Albers, Willem; Boon, Pieta C.; Kallenberg, Wilbert C. M. Size and power of pretest procedures. Ann. Statist., Tome 28 (2000) no. 3, pp. 195-214. http://gdmltest.u-ga.fr/item/1016120369/