Communications for Statistical Applications and Methods

  • 제22권6호
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  • Pages.639-646
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  • 2015
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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Simultaneous Tests with Combining Functions under Normality

  • Park, Hyo-Il (Department of Statistics, Chongju University)
  • 투고 : 2015.08.17
  • 심사 : 2015.10.06
  • 발행 : 2015.11.30
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초록

We propose simultaneous tests for mean and variance under the normality assumption. After formulating the null hypothesis and its alternative, we construct test statistics based on the individual p-values for the partial tests with combining functions and derive the null distributions for the combining functions. We then illustrate our procedure with industrial data and compare the efficiency among the combining functions with individual partial ones by obtaining empirical powers through a simulation study. A discussion then follows on the intersection-union test with a combining function and simultaneous confidence region as a simultaneous inference; in addition, we discuss weighted functions and applications to the statistical quality control. Finally we comment on nonparametric simultaneous tests.

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참고문헌

  1. Berger, R. L. (1996). Likelihood ratio tests and intersection-union tests, Institute of Statistics Mimeo Series Number 2288, Department of Statistics, North Carolina State University, Raleigh, North Carolina.
  2. Bickel, P. J. and Doksum, K. A. (1977). Mathematical Statistics-Basic Ideas and Selected Topics, Holden-Day, San Francisco.
  3. Chen, G. and Cheng, S. W. (1998). Max chart: combining X-bar chart and S chart, Statistica Sinica, 8, 263-271.
  4. Choudhari, P., Kundu, D. and Misra, N. (2001). Likelihood ratio test for simultaneous testing of the mean and the variance of a normal distribution, Journal of Statistical Computation and Simulation, 71, 313-333. https://doi.org/10.1080/00949650108812151
  5. DeVor, R. E., Chang, T. and Sutherland, J.W. (1992). Statistical Quality Design and Control, Macmillan, New York.
  6. Duran, B. S., Tsai, W. S. and Lewis, T. O. (1976). A class of location-scale tests, Biometrika, 63, 173-176.
  7. Fisher, R. A. (1932). Statistical Methods for Research Workers, Fourth Edition, Oliver and Boyd, Edinburgh.
  8. Good, L. J. (2000). Permutation Tests-A Practical Guide to Resampling Methods for Testing Hypotheses, Wiley, New York.
  9. Hawkins, D. M. and Deng, Q. (2009). Combined charts for mean and variance information, Journal of Quality Technology, 41, 415-425. https://doi.org/10.1080/00224065.2009.11917795
  10. Lepage, Y. (1971). A combination of Wilcoxon's and Ansari-Bradley's statistics, Biometrika, 58, 213-217. https://doi.org/10.1093/biomet/58.1.213
  11. Lepage, Y. (1973). A table for a combined Wilcoxon Ansari-Bradley statistic, Biometrika, 60, 113-116. https://doi.org/10.1093/biomet/60.1.113
  12. Liptak, I. (1958). On the combination of independent tests, Magyar Tudomanyos Akademia Matematikai Kutato Intezenek Kozlomenyei, 3, 127-141.
  13. Mood, A. M., Graybill, F. A. and Boes, D. C. (1974). Introduction to the Theory of Statistics, Third Edition (International Student Edition), McGraw-Hill, Tokyo.
  14. Murakami, H. (2007). Lepage type statistic based on the modified Baumgartner statistic, Computational Statistics & Data Analysis, 51, 5061-5067. https://doi.org/10.1016/j.csda.2006.04.026
  15. Neuhauser, M., Leuchs, A.-K. and Ball, D. (2011). A new location-scale test based on a combination of the ideas of Levene and Lepage, Biometrical Journal, 53, 525-534. https://doi.org/10.1002/bimj.201000162
  16. Park, H. I. (2012). On the study for the simultaneous test, Communications for Statistical Applications and Methods, 20, 241-246.
  17. Park, H. I. and Kim, J. S. (2012). A study on the bi-aspect procedure with location and scale parameters, Journal of The Korean Official Statistics, 17, 19-26.
  18. Park, H. I. and Han, K. J. (2013). A simultaneous test for mean and variance based on the likelihood ratio principle, Journal of the Korean Data Analysis Society, 15, 1733-1742.
  19. Pesarin, F. and Salmaso (2010). Permutation Tests for Complex Data, Wiley, New York.
  20. Roy, S. N. (1957). Some Aspects of Multivariate Analysis, Wiley, New York.
  21. Tippett, L. H. C. (1931). The Methods of Statistics, Williams and Norgate, London.