The behavior of locally most powerful tests

Marek Omelka

Kybernetika (2005)

  • Volume: 41, Issue: 6, page [699]-712
  • ISSN: 0023-5954

Abstract

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The locally most powerful (LMP) tests of the hypothesis H : θ = θ 0 against one-sided as well as two-sided alternatives are compared with several competitive tests, as the likelihood ratio tests, the Wald-type tests and the Rao score tests, for several distribution shapes and for location, shape and vector parameters. A simulation study confirms the importance of the condition of local unbiasedness of the test, and shows that the LMP test can sometimes dominate the other tests only in a very restricted neighborhood of H . Hence, we cannot recommend a universal application of the LMP tests in practice. The tests with a high Bahadur efficiency, though not exactly LMP, also seem to be good in the local sense.

How to cite

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Omelka, Marek. "The behavior of locally most powerful tests." Kybernetika 41.6 (2005): [699]-712. <http://eudml.org/doc/33782>.

@article{Omelka2005,
abstract = {The locally most powerful (LMP) tests of the hypothesis $H: \theta =\theta _0$ against one-sided as well as two-sided alternatives are compared with several competitive tests, as the likelihood ratio tests, the Wald-type tests and the Rao score tests, for several distribution shapes and for location, shape and vector parameters. A simulation study confirms the importance of the condition of local unbiasedness of the test, and shows that the LMP test can sometimes dominate the other tests only in a very restricted neighborhood of $H.$ Hence, we cannot recommend a universal application of the LMP tests in practice. The tests with a high Bahadur efficiency, though not exactly LMP, also seem to be good in the local sense.},
author = {Omelka, Marek},
journal = {Kybernetika},
keywords = {testing statistical hypothesis; locally most powerful tests},
language = {eng},
number = {6},
pages = {[699]-712},
publisher = {Institute of Information Theory and Automation AS CR},
title = {The behavior of locally most powerful tests},
url = {http://eudml.org/doc/33782},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Omelka, Marek
TI - The behavior of locally most powerful tests
JO - Kybernetika
PY - 2005
PB - Institute of Information Theory and Automation AS CR
VL - 41
IS - 6
SP - [699]
EP - 712
AB - The locally most powerful (LMP) tests of the hypothesis $H: \theta =\theta _0$ against one-sided as well as two-sided alternatives are compared with several competitive tests, as the likelihood ratio tests, the Wald-type tests and the Rao score tests, for several distribution shapes and for location, shape and vector parameters. A simulation study confirms the importance of the condition of local unbiasedness of the test, and shows that the LMP test can sometimes dominate the other tests only in a very restricted neighborhood of $H.$ Hence, we cannot recommend a universal application of the LMP tests in practice. The tests with a high Bahadur efficiency, though not exactly LMP, also seem to be good in the local sense.
LA - eng
KW - testing statistical hypothesis; locally most powerful tests
UR - http://eudml.org/doc/33782
ER -

References

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