Skip to main content

A Combinatorial Method in Robustness Research and Two Applications

  • Chapter
  • 281 Accesses

Part of the book series: Theory and Decision Library ((TDLB,volume 1))

Abstract

After defining robustness for interval estimations and tests, the paper presents an exact method for investigating this property for discrete distributions with finite supports. This method is used to investigate the u- and t-tests in the case of the single sample problem for robustness in respect of two and three point distributions.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Bickel, P. J. Another look at Robustness: A review of reviews and some new developments. Scand. J. Statist, 3 (1976), 145–168.

    MathSciNet  MATH  Google Scholar 

  • Guiard, G. (ed.) Robustheit II. Arbeitsmaterial zum Forschungsthema Robustheit. Probleme der angewandten Statistik (1981) 5.

    Google Scholar 

  • Herrendörfer, G. (ed.) Robustheit I. Arbeitsmaterial zum Forschungsthema Robustheit. Probleme der angewandten Statistik (1980) 4.

    Google Scholar 

  • Herrendörfer, G., Rasch, D., Feige, K.-D. Robustness of satistical methods II. Methods for the ons sample problem. Biom. Journ. 25 (1983) 327–343.

    MATH  Google Scholar 

  • Ito, K. Robustness of ANOVA and MANOVA test procedures. Handbook of Statistics, I (P. R. Krishnaiah, Ed.). North-Holland Publishing Company (1980), 199–236.

    Google Scholar 

  • Mandelbrot, B. The role of sufficiency and of estimation in thermodynamics. Ann. Math. Statist. 33 (1962), 1021–1038.

    Article  MathSciNet  MATH  Google Scholar 

  • Posten, H. O. The robustness of the two-sample t-test over the Pearson system. J. Stat. Comp. Simul., 6 (1978), 295–311.

    Article  MATH  Google Scholar 

  • Posten, H. O. The robustness of the one-sample t-test over the Pearson system. J. Statist. Comp. Simul. 9 (1979), 133–149.

    Article  MATH  Google Scholar 

  • Rasch, D. und Herrdörfer, G. (ed.) Robustheit III. Arbeitsmaterial zum Forschungsthema Rebustheit. Probleme der angewandten Statistik (1982) 7.

    Google Scholar 

  • Rey, W. J. J. Robust statistical methods. Springer Verlag Berlin (1978), Berlin — Heidelberg — NewYork: Springer Verlag 1978.

    Google Scholar 

  • Rider, P. R. On the distribution of the ratio of mean to standard deviation in small samples from non normal universes. Biometrika 21 (1929), 124–143.

    MATH  Google Scholar 

  • Tan, W. Y. Sampling distributions and robustness of t, F and variance ratio in two samples and ANOVA models with respect to departure from normality. Memphis State University, 1982, 28 Seiten.

    Google Scholar 

  • Tiku, M. L. Languerre series forms of the distributions of classical test-statistics and their robustness in nonnormal situations. Applied Statistics. (R. P. Gupta, Ed.) American Elsevier Pub., Comp., NewYork, 1975.

    Google Scholar 

  • Tukey, J. W. Where do we go from here? J. Amer. Statist. Ass. 55 (1960), 80–93.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Academy of Agricultural Sciences of the GDR, Research Centre of Animal Production, Dummerstorf-Rostock, DDR 2551 Dummerstorf.

About this chapter

Cite this chapter

Herrendörfer, G., Feige, KD. (1984). A Combinatorial Method in Robustness Research and Two Applications. In: Rasch, D., Tiku, M.L. (eds) Robustness of Statistical Methods and Nonparametric Statistics. Theory and Decision Library, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6528-7_12

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-6528-7_12

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-6530-0

  • Online ISBN: 978-94-009-6528-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics