Advertisement

Statistics and Computing

, Volume 11, Issue 2, pp 147–154 | Cite as

A permutation test for randomness with power against smooth variation

  • Fernando Tusell
Article

Abstract

A permutation test for the white noise hypothesis is described, offering power against a general class of smooth alternatives. Simulation results show that it performs well, as compared with similar tests available in the literature, in terms of power. An example demonstrates its use in a particular problem in which a test for randomness was sought without any specific alternative.

randomness serial independence permutation tests computer intensive tests smoothing complexity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aerts M., Claeskens G., and Hart J. 1998. Testing the fit of a parametric function. Unpublished manuscript.Google Scholar
  2. Bowman A. and Azzalini A. 1997. Applied Smoothing Techniques for Data Analysis. Oxford Univ. Press.Google Scholar
  3. Buckley M. 1991. Detecting a smooth signal: Optimality of cusum based procedures. Biometrika78: 253-262.Google Scholar
  4. Cox D., Koh E., Wahba G., and Yandell B. 1988. Testing the (parametric) null model hypothesis in (semiparametric) partial and generalized spline models. Annals of Statistics 16: 113-119.Google Scholar
  5. Craven P. and Wahba G. 1979. Smoothing noisy data with spline functions. Numerische Mathematik 31: 377-403.Google Scholar
  6. González-Manteiga W. and Cao R. 1993. Testing the hypothesis of a general linear model using nonparametric regression estimation. Test 2: 161-188.Google Scholar
  7. Gutiérrez J. and Tusell F. 1997. Suicides and the lunar cycle. Psychological Reports 80: 243-250.Google Scholar
  8. Härdle W. 1990. Smoothing Techniques with Implementations in S. Springer Verlag: New York.Google Scholar
  9. Hart J. 1997. Nonparametric Smoothing and Lack of Fit Tests. Springer Verlag: New York.Google Scholar
  10. Hastie T. and Tibshirani R. 1991. Generalized Additive Models, 2nd Edn. Chapman amp; Hall: London.Google Scholar
  11. Hurvich C.F., Simonoff J.S., and Tsai C.L. 1998. Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. Journal of the Royal Statistical Society, Ser. B 60: 271-293.Google Scholar
  12. Hutchinson M.F. 1986. Cubic spline data smoother. ACM Transactions of Mathematical Software 12:150-153. Software available at http://www.acm.org/calgo/contents/.Google Scholar
  13. Ramil L. and González-Manteiga W. 1998. Chi square goodness-of-fit tests for polynomial regression. Commun. Statistics—Simulation, 27: 229-258.Google Scholar
  14. Raz J. 1990. Testing for no effect when estimating a smooth function by nonparametric regression: A randomization approach. Journal of the American Statistical Association 85: 132-138.Google Scholar
  15. Rice J. 1984. Bandwidth choice for nonparametric regression. Annals of Statistics 12: 1215-1230.Google Scholar
  16. Rissanen J. 1989. Stochastic Complexity in Statistical Inquiry. World Scientific: Singapore.Google Scholar
  17. Silverman B.W. 1984.Spline smoothing: The equivalent variable kernel method. Annals of Statistics 12: 898-916.Google Scholar
  18. von Neumann J. 1941. Distribution of the ratio of the mean squared successive difference to the variance. Annals of Mathematical Statistics 12: 367-395.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Fernando Tusell
    • 1
  1. 1.Facultad de CC.EE. y EmpresarialesDepartamento de Estadística y EconometríaBilbaoSpain

Personalised recommendations