On the asymptotic power of a method for testing hypothesis about equality of distributions
DOI:
https://doi.org/10.21638/spbu01.2023.206Abstract
The paper is devoted to studying the asymptotic power of a method for testing hypothesis on equality of two distributions that can be considered as a generalization of Mann - Whitney -Wilcoxon test. We consider a class of distributions such that the expection of the square of an auxiliary function is finite. For the case when alternative distribution differ from the initial one only by a shift the asymptotic distribution and asymptotic power of the test are found explicitly. Up to now the power of the test was studied only by stochastic simulation.Keywords:
testing hypothesis on equality of two distributions, asymptotic power of statististical tests, Normal distribution Cashy distribution
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References
Литература
1. Zech G., Aslan B. New test for the multivariate two-sample problem based on the concept of minimum energy. Journal of Statistical Computation and Simulation 75 (2), 109-119 (2005).
2. Melas V., Salnikov D. On Asymptotic Power of the New Test for Equality of Two Distributions. In: Recent Developments in Stochastic Methods and Applications, vol. 371, 204-214. Springer Proceedings in Mathematics and Statistics (2021).
3. Леман Э. Л. Проверка статистических гипотез, пер. с англ. Москва, Наука (1979).
4. Buening H. Kolmogorov - Smirnov and Cramer - von Mises type two-sample tests with various weight functions. Communications in Statistics-Simulation and Computation 30, 847-865 (2001).
5. Anderson T.W., Darling D. A. A test of goodness-of-fit. J. Am. Stat. Assoc. 49, 765-769 (1954).
6. Hoeffding W. A class of statistics with asymptotically normal distribution. Ann. Math. Statistics 19, 293-325 (1948).
References
1. Zech G., Aslan B. New test for the multivariate two-sample problem based on the concept of minimum energy. Journal of Statistical Computation and Simulation 75 (2), 109-119 (2005).
2. Melas V., Salnikov D. On Asymptotic Power of the New Test for Equality of Two Distributions. In: Recent Developments in Stochastic Methods and Applications, vol. 371, 204-214. Springer Proceedings in Mathematics and Statistics (2021).
3. Lehmann Е. L. Testing statistical hypothess. New York, Yohn Wiley & Sons (1959) [Rus. ed.: Lehmann Е. L. Proverka statisticheskikh gipotez. Moscow, Nauka Publ. (1979)].
4. Buening H. Kolmogorov - Smirnov and Cramer - von Mises type two-sample tests with various weight functions. Communications in Statistics-Simulation and Computation 30, 847-865 (2001).
5. Anderson T.W., Darling D. A. A test of goodness-of-fit. J. Am. Stat. Assoc. 49, 765-769 (1954).
6. Hoeffding W. A class of statistics with asymptotically normal distribution. Ann. Math. Statistics 19, 293-325 (1948).
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Published
2023-05-10
How to Cite
Melas, V. B. (2023). On the asymptotic power of a method for testing hypothesis about equality of distributions. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 10(2), 249–258. https://doi.org/10.21638/spbu01.2023.206
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Section
Mathematics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
