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On the Study for the Simultaneous Test

  • Park, Hyo-Il (Department of Statistics, Chongju University)
  • 투고 : 2012.10.22
  • 심사 : 2013.05.29
  • 발행 : 2013.07.31

초록

In this study, we propose a nonparametric simultaneous test procedure for the location translation and scale parameters. We consider the Wilcoxon rank sum test for the location translation parameter and the Mood test for the scale parameter with the quadratic and maximal types of combining functions. Then we derive the limiting null distributions of the combining functions. We illustrate our procedure with an example and compare efficiency by obtaining the empirical powers through a simulation study. Finally, we discuss some interesting features related to the nonparametric simultaneous tests.

키워드

참고문헌

  1. Bickel, P. J. and Doksum, K. A. (1977). Mathematical Statistics-Basic Ideas and Selected Topics, Holden-Day, San Francisco.
  2. Fisher, R. A. (1925). Statistical Methods for Research Workers, Oliver & Boyd, Edinburgh.
  3. Good, P. (2000). Permutation Tests-A Practical Guide to Resampling Methods for Testing Hypotheses, Springer, New York.
  4. 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
  5. 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
  6. Milton, J. S. and Arnold, J. C. (2003). Introduction to Probability and Statistics: Principles and Applications for Engineering and the Computing Sciences, 4th ed. McGraw-Hill, Boston.
  7. Moser, B. K. and Stevens, G. R. (1992). Homogeneity of variance in the two-sample means test, The American Statistician, 46, 19-21.
  8. Murakami, H. (2007). Lepage type statistic based on the modified Baumgartner statistic, Computational Statistics and Data Analysis, 51, 5061-5067. https://doi.org/10.1016/j.csda.2006.04.026
  9. 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
  10. Pesarin, F. (2001). Multivariate Permutation Tests with Applications in Biostatistics, Wiley, New York.
  11. Randles, R. H. and Wolfe, D. A. (1979). Introduction to the Theory of Nonparametric Statistics, Wiley, New York.
  12. Rublik, F. (2009). Critical values for testing location-scale hypothesis, Measurement Science Review, 9, 9-15.

피인용 문헌

  1. Simultaneous Test for the Mean and Variance With an Application to the Statistical Process Control vol.9, pp.4, 2015, https://doi.org/10.1080/15598608.2015.1034387
  2. A Simultaneous Test Procedure vol.21, pp.1, 2014, https://doi.org/10.5351/CSAM.2014.21.1.011