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The behavior of locally most powerful tests
Kybernetika, Tome 41 (2005) no. 6, pp. 699-712 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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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     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, pp. 699-712. http://geodesic.mathdoc.fr/item/KYB_2005_41_6_a1/

[1] Brown L. D., Marden J. M.: Local admissibility and local unbiasedness in hypothesis testing problems. Ann. Statist. 20 (1992), 832–852 | DOI | MR | Zbl

[2] Chibisov D. M.: Asymptotic expansions for some asymptotically pptimal tests. In: Proc. Prague Symp. on Asymptotic Statistics, Volume II (J. Hájek, ed.), Charles University, Prague 1973, pp. 37–68 | MR

[3] Efron B.: Defining the curvature of a statistical problem (with application to second order efficiency). Ann. Statist. 3 (1975), 1189–1242 | DOI | MR

[4] Gupta A. S., Vermeire L.: Locally optimal tests for multiparameter hypotheses. J. Amer. Statist. Assoc. 81 (1986), 819–825 | DOI | MR | Zbl

[5] Isaacson S. L.: On the theory of unbiased tests of simple statistical hypothesis specifying the values of two or more parameters. Ann. Math. Statist. 22 (1951), 217–234 | DOI | MR

[6] Jurečková J.: $L_1$-derivatives, score function and tests. In: Statistical Data Analysis Based on the $L_1$-Norm and Related Methods (Y. Dodge, ed.), Birkhäuser, Basel 2002, pp. 183–189

[7] Kallenberg W. C. M.: The shortcomming of locally most powerful test in curved exponential families. Ann. Statist. 9 (1981), 673–677 | DOI | MR

[8] Lehmann E. L.: Testing Statistical Hypothesis. Second edition. Chapman & Hall, New York 1994

[9] Littel R. C., Folks J. L.: A test of equality of two normal population means and variances. J. Amer. Statist. Assoc. 71 (1976), 968–971 | DOI | MR

[10] Peers H. W.: Likelihood ratio and associated test criteria. Biometrika 58 (1971), 577–587 | DOI | Zbl

[11] Ramsey F. L.: Small sample power functions for nonparametric tests of location in the double exponential family. J. Amer. Statist. Assoc. 66 (1971), 149–151 | DOI | Zbl

[12] Witting H.: Mathematische Statistik I. Teubner–Verlag, Stuttgart 1985 | MR | Zbl

[13] Wong P. G., Wong S. P.: A curtailed test for the shape parameter of the Weibull distribution. Metrika 29 (1982), 203–209 | DOI | MR | Zbl