57
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

Logarithmic Quantile Estimation for Rank Statistics

&
Pages 146-170 | Received 27 May 2013, Accepted 18 Jan 2014, Published online: 03 Jul 2014

References

  • Akritas, M. G., and S. F. Arnold. 1994. Fully nonparametric hypotheses for factorial designs I: multivariate repeated measures designs. J. Am. Stat. Assoc., 89, 336–343.
  • Akritas, M. G., S. F. Arnold, and E. Brunner. 1997. Nonparametric hypotheses and rank statistics for unbalanced factorial designs. J. Am. Stat. Assoc., 92, 258–265.
  • Babu, G. J., and A. R. Padmanabhan. 2002. Re-sampling methods for the nonparametric Behrens–Fisher problem. Sankhyā Indian J. Stat., Ser. A, 64, 678–692.
  • Berkes, I., and E. Csáki. 2001. A universal result in almost sure central limit theory. Stochastic Processes Their Appl., 94, 105–134.
  • Berkes, I., and H. Dehling. 1993. Some limit theorems in log density. Ann. Probability, 21, 1640–1670.
  • Boos, D. D. 1986. Comparing K populations with linear rank statistics. J. Am. Stat. Assoc., 81(396), 1018–1025.
  • Brosamler, G. A. 1988. An almost everywhere central limit theorem. Math. Proc. Cambridge Philos. Soc., 104, 561–574.
  • Brunner, E., and M. Denker. 1994. Rank statistics under dependent observations and applications to factorial designs. J. Stat. Plan. Inference, 42, 353–378.
  • Brunner, E., and U. Munzel. 2000. The nonparametric Behrens–Fisher problem: Asymptotic theory and a small-sample approximation. Biometr. J., 42, 17–23.
  • Brunner, E., and M. L. Puri. 1996. Nonparametric methods in design and analysis of experiments. In Handbook of statistics, Vol. 13, 631–703. Amsterdam, The Netherlands: Elsevier Science.
  • Brunner, E., and M. L. Puri. 2002. A class of rank-score tests in factorial designs. J. Stat. Plan. Inference, 103, 331–360.
  • Chuprunov, A., and I. Fazekas. 2004. Almost sure limit theorems for the Pearson statistic. Theory Probab. Appl., 48, 14–147.
  • Denker, M., and M. Fridline. 2010. The almost sure version of Cramer’s theorem. In Dependence in probability, analysis and number theory, 195–201. Heber City, UT: Kendrick Press.
  • Devroye, L. 1986. Non-uniform random variate generation. New York, NY: Springer-Verlag.
  • Efron, B. 1979. Bootstrap methods: Another look at the jackknife. Ann. Stat., 7, 1–26.
  • Fridline, M. 2009. Almost sure confidence intervals for the correlation coefficient. Ph.D. thesis, Case Western Reserve University, Cleveland, OH.
  • Gentle, J. 2003. Random number generation and Monte Carlo methods. New York, NY: Springer-Verlag.
  • Holzmann, H., S. Koch, and A. Min. 2004. Almost sure limit theorems for U-statistics. Stat. Probability Lett., 69, 261–269.
  • Lacey, M. T., and W. Philipp. 1990. A note on the almost sure central limit theorem. Stat. Probability Lett., 9, 201–205.
  • Lifshits, M. A. 2002. The almost sure limit theorem for sums of random vectors. J. Math. Sci., 109(6), 2166–2178.
  • Lifshits, M. A. 2001. Lecture notes on almost sure limit theorems. Publications IRMA, Lille, 54, No. 8, 1–23.
  • Munzel, U. 1999. Linear rank score statistics when ties are present. Stat. Probability Lett., 41, 389–395.
  • Nation, J. R., A. E., Bourgeois, D. E., Clark, D. M., Baker, and M. F. Hare. 1984. The effects of oral cadmium exposure on passive avoidance performance in the adult rat. Toxicol. Lett., 20, 41–47.
  • Neuhäuser, M. 2012. Nonparametric statistical tests: A computational approach. Boca Raton, FL: Chapman & Hall, CRC Press.
  • Peligrad, M., and Q. M. Shao. 1995. A note on the almost sure central limit theorem for weakly dependent random variables. Stat. Probability Lett., 22, 131–136.
  • Reiczigel, J., I. Zakariàs, and L. Rózsa. 2005. A bootstrap test of stochastic equality of two populations. Am. Stat., 59, 156–161.
  • Schatte, P. 1988. On strong versions of the central limit theorem. Math. Nachricht., 137, 249–256.
  • Singh, R. S. 1975. On the Glivenko–Cantelli theorem for weighted empiricals based on independent random variables. Ann. Probability, 3, 371–374.
  • Steland, A. 1998. Bootstrapping rank statistics. Metrika, 47, 251–264.
  • Thangavelu, K. 2005. Quantile estimation based on the almost sure central limit theorem. Ph.D. thesis, Göttingen University, Göttingen, Germany.
  • Zöfel, P. 1992. Univariate Varianzanalysen. Uni-Taschenbuch 1663, G. Fischer Verlag, Jena, Stuttgart.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.