Power comparisons of the unbiased Berk-Jones test and the unbiased reversed Berk-Jones test

References

• Aldor-Noiman, S., L. D. Brown, A. Buja, W. Rolke, and R. A. Stine. 2013. The power to see: A new graphical test of normality. The American Statistician 67 (4):249–60.
   Web of Science ®Google Scholar
• Berk, R. H., and D. H. Jones. 1979. Goodness-of-fit test statistics that dominate the Kolmogorov statistics. Zeitschrift für Wahrscheinlichkeitstheorie Und Verwandte Gebiete 47 (1):47–59. doi: 10.1007/BF00533250.
   Google Scholar
• Ding, X., X. Xu, and S. Zhao. 2010. On exactness and unbiasedness of confidence bands for a continuous distribution function. Science China Mathematics 53 (10):2665–78. doi: 10.1007/s11425-010-4034-3.
   Web of Science ®Google Scholar
• Dümbgen, L., and J. A. Wellner. 2014. Confidence bands for distribution functions: A new look at the law of the iterated logarithm. Preprint, https://arxiv.org/pdf/1402.2918.
   Google Scholar
• Gibbons, J. D., and S. Chakraborti. 2010. Nonparametric statistical inference. 5th ed. Boca Raton, FL: CRC Press.
   Google Scholar
• Frey, J. 2009. Unbiased goodness-of-fit. Journal of Statistical Planning and Inference 139 (10):3690–7. doi: 10.1016/j.jspi.2009.04.017.
   Web of Science ®Google Scholar
• Jager, L., and J. A. Wellner. 2004. A new goodness of fit test: The reversed Berk-Jones statistics. Technical report. Washington, DC: Department of Statistics, University of Washington.
   Google Scholar
• Jager, L., and J. A. Wellner. 2007. Goodness-of-fit tests via phi-divergences. The Annals of Statistics 35 (5):2018–53. doi: 10.1214/0009053607000000244.
   Web of Science ®Google Scholar
• Lehmann, E. L. 1951. Consistency and unbiasedness of certain nonparametric tests. The Annals of Mathematical Statistics 22 (2):165–79. doi: 10.1214/aoms/1177729639.
   Google Scholar
• Lehmann, E. L., and J. P. Romano. 2005. Testing statistical hypotheses. 3rd ed. New York: Springer.
   Google Scholar
• Massey, F. J. 1950. A note on the power of a non-parametric test. The Annals of Mathematical Statistics 21 (3):440–3. doi: 10.1214/aoms/1177729803.
   Google Scholar
• Moscovich-Eiger, A., B. Nadler, and C. Spiegelman. 2014. The calibrated Kolmogorov-Smirnov test. Cornell University arXiv. Preprint, https://arxiv.org/abs/1311.3190v3.
   Google Scholar
• Murakami, H., and S.-K. Lee. 2015. Unbiasedness and biasedness of the Jonckheere-Terpstra and the Kruskal-Wallis tests. Journal of the Korean Statistical Society 44 (3):342–51. doi: 10.1016/j.jkss.2014.10.001.
   Web of Science ®Google Scholar
• Murakami, H., and S.-K. Lee. 2017. The unbiased nonparametric test and its moment generating function for the order alternative. Statistics and Probability Letters 126:193–7. doi: 10.1016/j.spl.2017.03.009.
   Web of Science ®Google Scholar
• Neuhäuser, M., A. Welz, and G. D. Ruxton. 2017. Statistical tests for the comparison of two samples: The general alternative. Communications in Statistic–Simulation and Computation 46 (2):903–9. doi: 10.1080/03610918.2014.983651.
   Web of Science ®Google Scholar
• Noé, M. 1972. The calculation of distributions of two-sided Kolmogorov-Smirnov type statistics. The Annals of Mathematical Statistics 43:58–64.
   Google Scholar
• Owen, A. 1995. Nonparametric likelihood confidence band for a distribution function. Journal of the American Statistical Association 90 (430):516–21. doi: 10.1080/01621459.1995.10476543.
   Web of Science ®Google Scholar
• Sugiura, N. 1965. An example of the two-sided Wilcoxon test which is not unbiased. Annals of the Institute of Statistical Mathematics 17 (1):261–3. doi: 10.1007/BF02868170.
   Google Scholar
• Sugiura, N., H. Murakami, S.-K. Lee, and Y. Maeda. 2006. Biased and unbiased two-sided Wilcoxon tests for equal sample sizes. Annals of the Institute of Statistical Mathematics 58 (1):93–100. doi: 10.1007/s10463-005-0019-3.
   Web of Science ®Google Scholar
• Thompson, R. 1966. Bias of the one-sample Cramér-Von Mises test. Journal of the American Statistical Association 61:246–7. doi: 10.1080/01621459.1966.10502023.
   Web of Science ®Google Scholar
• Wellner, J. A., and V. Koltchinskii. 2003. A note on the asymptotic distribution of Berk-Jones type statistics under the null hypothesis. High Dimensional Probability III, Vol. 55, 321–332.
   Google Scholar
• Xu, X., X. Ding, and S. Zhao. 2009. A new confidence band for continuous cumulative distribution functions. Australian & New Zealand Journal of Statistics 51 (3):305–18. doi: 10.1111/j.1467-842X.2009.00546.x.
   Web of Science ®Google Scholar
• Xu, X., X. Ding, and S. Zhao. 2009. The reduction of the average width of confidence bands for an unknown continuous distribution function. Journal of Statistical Computation and Simulation 79 (4):335–47. doi: 10.1080/00949650701763464.
   Web of Science ®Google Scholar