Geodesic
The behavior of locally most powerful tests
Kybernetika, Tome 41 (2005) no. 6, p. [699].

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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.
Classification : 62F03, 65C60
Keywords: testing statistical hypothesis; locally most powerful tests 
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     author = {Omelka, Marek},
     title = {The behavior of locally most powerful tests},
     journal = {Kybernetika},
     pages = {[699]},
     publisher = {mathdoc},
     volume = {41},
     number = {6},
     year = {2005},
     mrnumber = {2193860},
     zbl = {1244.62018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2005__41_6_a1/}
}
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Omelka, Marek. The behavior of locally most powerful tests. Kybernetika, Tome 41 (2005) no. 6, p. [699]. http://geodesic.mathdoc.fr/item/KYB_2005__41_6_a1/