Advertisement

Permutation Tests and the Bootstrap

  • Kenneth Lange
Chapter
Part of the Statistics and Computing book series (SCO)

Abstract

In this chapter we discuss two techniques, permutation testing and the bootstrap, of immense practical value. Both techniques involve random resampling of observed data and liberate statisticians from dubious model assumptions and large sample requirements. Both techniques initially met with considerable intellectual resistance. The notion that one can conduct hypothesis tests or learn something useful about the properties of estimators and confidence intervals by resampling data was alien to most statisticians of the past. The computational demands of permutation testing and bootstrapping alone made them unthinkable. These philosophical and practical objections began to crumble with the advent of modern computing.

Keywords

Permutation Test Importance Sampling Edgeworth Expansion Multivariate Observation Antenna Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Babu GJ, Singh K (1984) On a one term Edgeworth correction for Efron’s bootstrap. Sankhya A 46:219-232MATHMathSciNetGoogle Scholar
  2. 2.
    Bickel PJ, Freedman DA (1981) Some asymptotics for the bootstrap. Ann Stat 9:1196-1217MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bradley JV (1968). Distribution-Free Statistical Tests. Prentice-Hall, Englewood Cliffs, NJMATHGoogle Scholar
  4. 4.
    Davison AC (1988) Discussion of papers by DV Hinkley and TJ DiCi- ccio and JP Romano. J Roy Stat Soc B 50:356-357MathSciNetGoogle Scholar
  5. 5.
    Davison AC, Hinkley DV (1997) Bootstrap Methods and Their Applications. Cambridge University Press, CambridgeGoogle Scholar
  6. 6.
    Davison AC, Hinkley DV, Schechtman E (1986) Efficient bootstrap simulation. Biometrika 73:555-566MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Efron B (1979) Bootstrap methods: Another look at the jackknife. Ann Stat 7:1-26MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Efron B (1987) Better bootstrap confidence intervals (with discussion). J Amer Stat Assoc 82:171-200MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Efron B, Tibshirani RJ (1993) An Introduction to the Bootstrap. Chapman & Hall, New YorkMATHGoogle Scholar
  10. 10.
    Ernst MD (2004) Permutation methods. Stat Sci 19:676-685MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Fisher RA (1935) The Design of Experiments. Hafner, New YorkGoogle Scholar
  12. 12.
    Givens GH, Hoeting JA (2005) Computational Statistics. Wiley, Hoboken, NJMATHGoogle Scholar
  13. 13.
    Gleason JR (1988) Algorithms for balanced bootstrap simulations. Amer Statistician 42:263-266CrossRefGoogle Scholar
  14. 14.
    Grogan WL, Wirth WW (1981) A new American genus of predaceous midges related to Palpomyia and Bezzia (Diptera: Ceratopogonidae). Proc Biol Soc Wash 94:1279-1305Google Scholar
  15. 15.
    Hall P (1989) Antithetic resampling for the bootstrap. Biometrika 76:713-724MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Hall P (1992) The Bootstrap and Edgeworth Expansion. Springer, New YorkGoogle Scholar
  17. 17.
    Johns MV Jr (1988) Importance sampling for bootstrap confidence intervals. J Amer Stat Assoc 83:709-714MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Lazzeroni LC, Lange K (1997) Markov chains for Monte Carlo tests of genetic equilibrium in multidimensional contingency tables. Ann Stat 25:138-168MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Ludbrook J, Dudley H (1998) Why permutation tests are superior to t and F tests in biomedical research. Amer Statistician 52:127-132CrossRefGoogle Scholar
  20. 20.
    Nijenhuis A, Wilf HS (1978) Combinatorial Algorithms for Computers and Calculators, 2nd ed. Academic Press, New YorkMATHGoogle Scholar
  21. 21.
    Peressini AL, Sullivan FE, Uhl JJ Jr (1988) The Mathematics of Nonlinear Programming. Springer, New YorkMATHGoogle Scholar
  22. 22.
    Pitman EJG (1937) Significance tests which may be applied to samples from any population. J Roy Stat Soc Suppl 4:119-130CrossRefGoogle Scholar
  23. 23.
    Pitman EJG (1937) Significance tests which may be applied to samples from any population. II. The correlation coefficient test. J Roy Stat Soc Suppl 4:225-232CrossRefGoogle Scholar
  24. 24.
    Pitman EJG (1938) Significance tests which may be applied to samples from any population. III. The analysis of variance test. Biometrika 29:322-335MATHGoogle Scholar
  25. 25.
    Quenouille M (1949) Approximate tests of correlation in time series. J Roy Stat Soc Ser B 11:18-44MathSciNetGoogle Scholar
  26. 26.
    Serfling RJ (1980) Approximation Theorems in Mathematical Statistics. Wiley, New YorkCrossRefGoogle Scholar
  27. 27.
    Shao J, Tu D (1995) The Jackknife and Bootstrap. Springer, New YorkMATHGoogle Scholar
  28. 28.
    Snee RD (1974) Graphical display of two-way contingency tables. Amer Statistician 38:9-12CrossRefGoogle Scholar
  29. 29.
    Tukey JW (1958) Bias and confidence in not quite large samples. (Abstract) Ann Math Stat 29:614CrossRefGoogle Scholar

Copyright information

© Springer New York 2010

Authors and Affiliations

  1. 1.Departments of Biomathematics, Human Genetics, and Statistics David Geffen School of MedicineUniversity of California, Los AngelesLos AngelesUSA

Personalised recommendations