On the power of criteria in the case of samples of random size
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2018), pp. 5-22 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper general theorem concerning the asymptotic expansions for the generalized power of the tests based on the sample with random size is proved. These results are closed connected with the concept of asymptotic deficiency and may be used for asymptotic comparison of different asymptotically equivalent tests. Some examples are presented.
Keywords: power of test, asymptotic deficiency, sample of random size, asymptotic expansions, three-point symmetric distribution.
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V. E. Bening. On the power of criteria in the case of samples of random size. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2018), pp. 5-22. http://geodesic.mathdoc.fr/item/VTPMK_2018_4_a0/

[1] Bening V. E., Asymptotic Theory of Testing Statistical Hypotheses: Efficient Statistics, Optimality, Power Loss, and Deficiency, VSP, Utrecht, 2000, 277 pp.

[2] Chibisov D. M., “Calculation of deficiency of asymptotically efficient tests”, Theory of Probability and its Applications, 30:2 (1986), 289–310 | DOI | MR | MR | Zbl

[3] Borovkov A. A., Probability Theory, Editorial URSS Publ., Moscow, 2003, 470 pp. (in Russian)

[4] Pfanzagl J., “Asymptotic expansions in parametric statistical theory”, Developments in Statistics, v. 3, ed. P.R. Krishnaiah, Academic Press, New York, 1980, 1–97 | MR

[5] Lehmann E. L., Romano J. P., Testing Statistical Hypotheses, Third edition, Springer, 2005, 784 pp. | MR | Zbl

[6] Nikitin Ya. Yu., Asymptotic Efficiency of Non-Parametric Criteria, Nauka Publ., Moscow, 1995, 250 pp. (in Russian)

[7] Pitman E. J. G., Lecture notes on nonparametric statistical inference, Lectures given for the University of North Carolina, Institute of Statistics, 1948

[8] Hodges J. L., Lehmann E. L., “Deficiency”, The Annals of Mathematical Statistics, 41:5 (1970), 783–801 | DOI | MR | Zbl

[9] Bickel P. J., “Edgeworth expansions in nonparametric statistics”, The Annals of Mathematical Statistics, 2:1 (1974), 1–20 | DOI | MR | Zbl

[10] Bickel P. J., Chibisov D. M., Van Zwet W. R., “On efficiency of first and second order”, International Statistical Review, 49 (1981), 169–175 | DOI | MR | Zbl

[11] Albers W., Bickel P. J., Van Zwet W. R., “Asymptotic expansions for the power of distribution free tests in the one – sample problem”, Annals of Statistics, 4:1 (1976), 108–156 | DOI | MR | Zbl

[12] Gnedenko B. V., “On the estimation of unknown distribution parameters for a random number of independent observations”, Proceedings of the Tbilisi Mathematical Institute, 92 (1989), 146–150 (in Russian) | Zbl

[13] Gnedenko B. V., Fakhim Kh., “On a transfer theorem”, Doklady Mathematics, 187 (1969), 15–17 (in Russian) | MR | Zbl

[14] Bening V. E., Korolev V. Y., “On an application of the Student distribution in the theory of probability and mathematical statistics”, Theory of Probability and its Applications, 49:3 (2005), 377–391 | DOI | MR | Zbl

[15] Bening V. E., Korolev V. Yu., Generalized Poisson Models and Their Applications in Insurance and Finance, VSP, Utrecht, 2002, 434 pp. | Zbl

[16] Bening V. E., Korolev V. Yu., “Some statistical problems related to the Laplace distribution”, Informatics and Applications, 2:2 (2008), 19–34 (in Russian)

[17] Bening V. E., “On deficiencies of some estimators based on samples of random size”, Herald of Tver State University. Series: Applied Mathematics, 2015, no. 1, 5–14 (in Russian)