Simultaneous Test for the Mean and Variance With an Application to the Statistical Process Control

References

• Alfieri, R., A. Bonnini, C. Brombin, C. Castro, and L. Salmaso. 2012. Iterated combination-based paired permutation tests to determine shape effects of chemotherapy in patients with esophageal cancer. Statistical Methods in Medical Research. doi:10.1177/0962280212461981
   PubMedGoogle Scholar
• Alloway, J. A., and M. Raghavachari. 1991. Control chart based on the Hodges–Lehmann estimator. Journal of Quality Technology 23: 336–47.
   Web of Science ®Google Scholar
• Arnold, B. C., and R. M. Shavelle. 1998. Joint confidence sets for the mean and variance of a normal distribution. American Statistician 52: 133–40.
   Web of Science ®Google Scholar
• Berger, R. L. 1996. Likelihood ratio tests and intersection–union tests. Raleigh, NC: Institute of Statistics Mimeo Series Number 2288, Department of Statistics, North Carolina State University.
   Google Scholar
• Bickel, P. J., and K. A. Doksum. 1977. Mathematical statisics. San Francisco, CA: Basic Ideas and Selected Topics, Holden-Day.
   Google Scholar
• Chao, M. T., and S. W. Cheng. 1996. Semicircle control chart for variables data. Quality Engineering 8: 441–46. doi:10.1080/08982119608904646
   Google Scholar
• Chen, G., and S. W. Cheng. 1998. Max chart: Combining X-bar chart and S chart. Statistica Sinica 8: 263–71.
   Web of Science ®Google Scholar
• Choudhari, P., D. Kundu, and N. Misra. 2001. Likelihood ratio test for simultaneous testing of the mean and the variance of a normal distribution. Journal of Statistical Computation and Simulation 71: 313–33. doi:10.1080/00949650108812151
   Web of Science ®Google Scholar
• Corain, L., and L. Salmaso. 2013. Nonparametric permutation and combination-based multivariate control charts with applications in microelectronics. Applied Stochastic Models in Business and Industry 29: 334–49. doi:10.1002/asmb.1976
   Web of Science ®Google Scholar
• Duran, B. S., W. S. Tsai, and T. O. Lewis. 1976. A class of location-scale tests. Biometrika 63: 173–76.
   Web of Science ®Google Scholar
• Fisher, R. A. 1932. Statistical methods for research workers, 4th ed. Edinburgh, UK: Oliver and Boyd.
   Google Scholar
• Frey, J., O. Marrero, and D. Norton. 2009. Minimum-area confidence sets for a normal distribution. Journal of Statistical Planning and Inference 139: 1023–32. doi:10.1016/j.jspi.2008.06.005
   Web of Science ®Google Scholar
• Hawkins, D. M., and Q. Deng. 2009. Combined charts for mean and variance information. Journal of Quality Technology 41:415–25.
   Web of Science ®Google Scholar
• Hayter, A. 2014. Identifying common normal distributions. Test 23: 135–52. doi:10.1007/s11749-013-0345-3
   Web of Science ®Google Scholar
• Kendall, M. G., and A. Stuart. 1961. The advanced theory of statistics, vol. 2. London, UK: Charles Griffin.
   Google Scholar
• Lepage, Y. 1971. A combination of Wilcoxon’s and Ansari-Bradley’s statistics. Biometrika 58: 213–17. doi:10.1093/biomet/58.1.213
   Web of Science ®Google Scholar
• Lepage, Y. 1973. A table for a combined Wilcoxon Ansari-Bradley statistic. Biometrika 60: 113–16. doi:10.1093/biomet/60.1.113
   Web of Science ®Google Scholar
• Mood, A. M., F. A. Graybill, and D. C. Boes. 1974. Introduction to the theory of statistics, 3rd. ed. (international student edition). Tokyo, Japan: McGraw-Hill.
   Google Scholar
• Neuhäuser, M., A.-K. Leuchs, and D. Ball. 2011. A new location-scale test based on a combination of the ideas of Levene and Lepage. Biometrical Journal 53: 525–34. doi:10.1002/bimj.201000162
   PubMed Web of Science ®Google Scholar
• Owen, A. B. 2009. Karl Pearson’s meta-analysis revisited. Annals of Statistics 37: 3867–92. doi:10.1214/09-AOS697
   Web of Science ®Google Scholar
• Park, H.-I. 2013. On the study for the simultaneous test. Communications for Statistical Applications and Methods 20: 241–46. doi:10.5351/CSAM.2013.20.4.241
   Google Scholar
• Pesarin, F., and L. Salmaso. 2010. Permutation tests for complex data. New York, NY: Wiley.
   Google Scholar
• Randles, R. H., and D. A. Wolfe. 1979. Introduction to the theory of nonparametric statistics. New York, NY: Wiley.
   Google Scholar
• Roy, S. N. 1957. Some aspects of multivariate analysis. New York, NY: Wiley.
   Google Scholar
• Rublik, F. 2009. Critical values for testing location-scale hypothesis. Em Measurement Science Review 9: 9–15.
   Web of Science ®Google Scholar
• Won, S., N. Morris, Q. Lu, and R. C. Elston. 2009. Choosing an optimal method to combine p-values. Statistics in Medicine 28: 1537–53. doi:10.1002/sim.v28:11
   PubMed Web of Science ®Google Scholar