It is shown that the global power function of any nonparametric test
is flat on balls of alternatives except for alternatives coming from a finite
dimensional subspace. The present benchmark is here the upper one-sided (or
two-sided) envelope power function. Every choice of a test fixes a priori a
finite dimensional region with high power. It turns out that also the level
points are far away from the corresponding Neyman–Pearson test level
points except for a finite number of orthogonal directions of alternatives. For
certain submodels the result is independent of the underlying sample size. In
the last section the statistical consequences and special goodness of fit tests
are discussed.
Publié le : 2000-02-14
Classification:
Goodness of fit test,
Kolmogorov–Smirnov test,
power function,
envelope power function,
curvature of power functions,
level points,
data driven Neyman’s smooth test,,
Pitman efficiency,
Bahadur efficiency,
intermediate efficiency.,
62G10,
62G20
@article{1016120371,
author = {Janssen, Arnold},
title = {Global power functions of goodness of fit tests},
journal = {Ann. Statist.},
volume = {28},
number = {3},
year = {2000},
pages = { 239-253},
language = {en},
url = {http://dml.mathdoc.fr/item/1016120371}
}
Janssen, Arnold. Global power functions of goodness of fit tests. Ann. Statist., Tome 28 (2000) no. 3, pp. 239-253. http://gdmltest.u-ga.fr/item/1016120371/