Advertisement

Tools for Nonparametric Statistics

  • Mayer Alvo
  • Philip L. H. Yu
Chapter
Part of the Springer Series in the Data Sciences book series (SSDS)

Abstract

Nonparametric statistics is concerned with the development of distribution free methods to solve various statistical problems. Examples include tests for a monotonic trend, or tests of hypotheses that two samples come from the same distribution. One of the important tools in nonparametric statistics is the use of ranking data. When the data is transformed into ranks, one gains the simplicity that objects may be more easily compared. For example, if web pages are ranked in accordance to some criterion, one obtains a quick summary of choices. In this chapter, we will study linear rank statistics which are functions of the ranks.

References

  1. Bhattacharya, R., Lizhen, L., and Patrangenaru, V. (2016). A Course in Mathematical Statistics and Large Sample Theory. Springer.Google Scholar
  2. Diaconis, P. and Graham, R. (1977). Spearman’s footrule as a measure of disarray. Journal of the Royal Statistical Society Series B, 39:262–268.MathSciNetzbMATHGoogle Scholar
  3. Ferguson, T. (1996). A Course in Large Sample Theory. John Wiley and Sons.CrossRefGoogle Scholar
  4. Gibbons, J. D. and Chakraborti, S. (2011). Nonparametric Statistical Inference. Chapman Hall, New York, 5th edition.CrossRefGoogle Scholar
  5. Gotze, F. (1987). Approximations for multivariate U statistics. Journal of Multivariate Analysis, 22:212–229.MathSciNetCrossRefGoogle Scholar
  6. Hajek, J. (1968). Asymptotic normality of simple linear rank statistics under alternatives. Ann. Math. Statist., 39:325–346.MathSciNetCrossRefGoogle Scholar
  7. Hájek, J. and Sidak, Z. (1967). Theory of Rank Tests. Academic Press, New York.zbMATHGoogle Scholar
  8. Hoeffding, W. (1948). A class of statistics with asymptotically normal distribution. Annals of Mathematical Statistics, 19:293–325.MathSciNetCrossRefGoogle Scholar
  9. Hoeffding, W. (1951a). A combinatorial central limit theorem. Annals of Mathematical Statistics, 22:558–566.MathSciNetCrossRefGoogle Scholar
  10. Lee, A. (1990). U-Statistics. Marcel Dekker Inc., New York.zbMATHGoogle Scholar
  11. Lehmann, E. (1975). Nonparametrics: Statistical Methods Based on Ranks. McGraw-Hill, New York.zbMATHGoogle Scholar
  12. Randles, Ronald, H. and Wolfe, Douglas, A. (1979). Introduction to the Theory of Nonparametric Statistics. John Wiley and Sons, Inc.Google Scholar
  13. van der Vaart, A. (2007). Asymptotic Statistics. Cambridge University Press.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Mayer Alvo
    • 1
  • Philip L. H. Yu
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of OttawaOttawaCanada
  2. 2.Department of Statistics and Actuarial ScienceUniversity of Hong KongHong KongChina

Personalised recommendations