Skip to main content
SpringerLink
Log in

22 An Upper Bound for the Variance of Kendall’s “Tau” and of Related Statistics

  • Chapter
The Collected Works of Wassily Hoeffding

Part of the book series: Springer Series in Statistics ((PSS))

Abstract

Let X 1, X 2, …, X n be independent and identically distributed random variables (real- or vector-valued). Let f(X 1, X 2) denote a bounded function such that f(X 1, X 2) =f(X 2, X 1). With no loss of generality we shall assume that the bounds are Let

This research was supported by the United States Air Force through the Air Force Office of Scientific Research, Air Research and Development Command, under Contract No. AF 18(600)-458. Reproduction in whole or in part is permitted for any purpose of the United States Government.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Hoeffding, W. A class of statistics with asymptotically normal. distribution. Ann. Math. Stat., 1948, 19, 293–325.

    Article  MathSciNet  MATH  Google Scholar 

  2. Kendall, M. G. Rank Correlation Methods, 2d ed. London: Griffin, New York: Hafner, 1955.

    MATH  Google Scholar 

  3. Daniels, H. E., and Kendall, M. G. The significance of rank correlations where parental correlation exists. Biometrika, 1947, 34, 197–208.

    MathSciNet  MATH  Google Scholar 

  4. Sundrum, R. M. Moments of the rank correlation coefficient τ in the general case. Biometrika, 1953, 40, 409–420.

    MathSciNet  MATH  Google Scholar 

  5. Walsh, J. E. Some significance tests for the median which are valid under very general conditions, Ann. Math. Stat., 1949, 20, 64–81.

    Article  MATH  Google Scholar 

  6. [Tukey, J. W.] The simplest signed-rank tests. Statistical Research Group Memorandum No. 17, Princeton, N.J.: Princeton University [No date].

    Google Scholar 

  7. Wilcoxon, F. Individual comparisons by ranking methods. Biometrics Bull., 1945, 1, 80–83.

    Article  Google Scholar 

  8. Dantzig, D. van. On the consistency and the power of Wilcoxon’s two sample test. Ned. Akad. Wetenschap. Proc., Ser. A, 1951, 54, 1–8.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of North Carolina, USA

    Wassily Hoeffding

Authors
  1. Wassily Hoeffding
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Division of Mathematics and Statisics, CSIRO, E6B, Macquarie University Campus, North Ryde, NSW, 2113, Australia

    N. I. Fisher

  2. Department of Statistics, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599, USA

    P. K. Sen

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Science+Business Media New York

About this chapter

Cite this chapter

Hoeffding, W. (1994). 22 An Upper Bound for the Variance of Kendall’s “Tau” and of Related Statistics. In: Fisher, N.I., Sen, P.K. (eds) The Collected Works of Wassily Hoeffding. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0865-5_23

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-0865-5_23

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6926-7

  • Online ISBN: 978-1-4612-0865-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation