The basic motivation and primary goal of this paper is a qualitative evaluation of the performance of a new weighted statistic for a nonparametric test for stochastic dominance based on two samples, which was introduced in Ledwina and Wyłupek [TEST 21 (2012) 730–756]. For this purpose, we elaborate a useful variant of Kallenberg’s notion of intermediate efficiency. This variant is general enough to be applicable to other nonparametric problems. We provide a formal definition of the proposed variant of intermediate efficiency, describe the technical tools used in its calculation, and provide proofs of related asymptotic results. Next, we apply this approach to calculating the intermediate efficiency of the new test with respect to the classical one-sided Kolmogorov–Smirnov test, which is a recognized standard for this problem. It turns out that for a very large class of convergent alternatives the new test is more efficient than the classical one. We also report the results of an extensive simulation study on the powers of the tests considered, which shows that the new variant of intermediate efficiency reflects the exact behavior of the power well.
Mots-clés : Anderson–Darling weight, asymptotic relative efficiency, goodness-of-fit, independence testing, Kallenberg efficiency, Kolmogorov–Smirnov test, local alternatives, moderate deviations, stochastic order, two-sample problem
@article{PS_2019__23__697_0,
author = {Inglot, Tadeusz and Ledwina, Teresa and \'Cmiel, Bogdan},
title = {Intermediate efficiency in nonparametric testing problems with an application to some weighted statistics},
journal = {ESAIM: Probability and Statistics},
pages = {697--738},
publisher = {EDP-Sciences},
volume = {23},
year = {2019},
doi = {10.1051/ps/2018022},
mrnumber = {4026482},
zbl = {1507.62250},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2018022/}
}
TY - JOUR AU - Inglot, Tadeusz AU - Ledwina, Teresa AU - Ćmiel, Bogdan TI - Intermediate efficiency in nonparametric testing problems with an application to some weighted statistics JO - ESAIM: Probability and Statistics PY - 2019 SP - 697 EP - 738 VL - 23 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2018022/ DO - 10.1051/ps/2018022 LA - en ID - PS_2019__23__697_0 ER -
%0 Journal Article %A Inglot, Tadeusz %A Ledwina, Teresa %A Ćmiel, Bogdan %T Intermediate efficiency in nonparametric testing problems with an application to some weighted statistics %J ESAIM: Probability and Statistics %D 2019 %P 697-738 %V 23 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2018022/ %R 10.1051/ps/2018022 %G en %F PS_2019__23__697_0
Inglot, Tadeusz; Ledwina, Teresa; Ćmiel, Bogdan. Intermediate efficiency in nonparametric testing problems with an application to some weighted statistics. ESAIM: Probability and Statistics, Tome 23 (2019), pp. 697-738. doi : 10.1051/ps/2018022. http://www.numdam.org/articles/10.1051/ps/2018022/
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