Wavelet Thresholding Methods Applied to Testing Significance Differences Between Autoregressive Hilbertian Processes

  • María Ruiz-Medina
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

The philosophy of Fan (1996) and Fan and Lin (1998) is adopted in the formulation of significance tests for comparing autoregressive Hilbertian processes. The discrete wavelet domain is considered to derive the test statistic based on thresholding rules. The results derived are applied to the statistical analysis of spatial functional data (SFD) sequences.


American Statistical Association Wavelet Domain Functional Data Analysis Hard Thresholding Thresholding Rule 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Abramovich, F. and Angelini, C.: Testing in mixed e ects FANOVA models. Journal of Statistical Planning and Inference. 136, 4326-4348 (2006).MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Abramovich, F., Antoniadis, A., Sapatinas, T. and Vidakovic, B.: Optimal testing in functional analysis of variance models. Int. J. Wavelets Multiresolution Inform. Process. 2, 323-349.Google Scholar
  3. [2]
    Angulo, J.M. and Ruiz-Medina, M.D. (1999). Multiresolution approximation to the stochastic inverse problem. Adv. App. Prob. 31, 1039-1057 (2004).MATHCrossRefMathSciNetGoogle Scholar
  4. [3]
    Bosq, D.: Linear processes in function spaces. Springer-Verlag. (2000).Google Scholar
  5. [4]
    Brillinger, D. R.: The analysis of time series collected in an experiment design. In Multivariate analysis, III. Krishnaiah, P.R. (ed.), Academic Press, 241-256 (1973).Google Scholar
  6. [5]
    Brillinger, D. R.: Some aspect of the analysis of evoked response experiments. In Statistics and related topics. Csörgö, M., Dawson, D.A. Rao, J.N.K. and Saleh, A.K. (eds.), North-Holland, 15-168 (1980).Google Scholar
  7. [6]
    Fan, J.: Test of signi cance based on wavelet thresholding and neyman 's truncation. Journal of American Statistical Association. 91, 674-688 (1996).MATHCrossRefGoogle Scholar
  8. [7]
    Fan, J. and Lin, S.J.: Test of signi cance when data are curves. Journal of American Statistical Association. 93, 1007-1021 (1998).MATHCrossRefMathSciNetGoogle Scholar
  9. [8]
    Ferraty, F. and Vieu, P.: Nonparameric functional data analysis. Springer. (2006).Google Scholar
  10. [9]
    Eubank, R.L. and Hart, J.D.: Testing goodness-of-t in regression via order selection criteria. The Annals of Statistics. 20, 1412-1425 (1992).MATHCrossRefMathSciNetGoogle Scholar
  11. [10]
    Eubank, R.L. and LaRiccia, V.N.: Asymptotic comparison of Cramér-von Mises and non-parametric function estimation techniques for testing goodness-of-t. The Annals of Statistics. 20, 2071-2086 (1992).MATHCrossRefMathSciNetGoogle Scholar
  12. [11]
    Guillas, S.: Rates of convergence of autocorrelation estimates for autoregressive Hilbertian processes. Stat. Prob. Lett. 55, 281-291 (2001).MATHCrossRefMathSciNetGoogle Scholar
  13. [12]
    Hall, P. and Hart, J.D.: Bootstrap test for di erence between means in nonparametric regression. Journal of American Statistical Association. 85, 1039-1049 (1990).MATHCrossRefMathSciNetGoogle Scholar
  14. [13]
    Inglot, T. and Ledwina, T.: Asymptotic optimality of data-driven Neyman's tests for uniformity. The Annals of Statistics. 24, 1982-2019 (1996).MATHCrossRefMathSciNetGoogle Scholar
  15. [14]
    Ledwina, T.: Data-driven version of Neyman's smooth test of t. Journal of American Statistical Association. 89, 1000-1005 (1994).MATHCrossRefMathSciNetGoogle Scholar
  16. [15]
    Maraun, D. and Kurths, J.: Cross-wavelet analysis: signi cance testing and pitfalls. Nonlinear Processes in Geophysics. 11, 505-514 (2004).Google Scholar
  17. [16]
    Maraun, D., Kurths, J. and Holschneider, M.: Nonstationary Gaussian processes in wavelet domain: Synthesis, estimation, and signi cance testing. Physical Review E. 5,016707-1-016707-14 (2007).CrossRefMathSciNetGoogle Scholar
  18. [17]
    Ruiz-Medina, M.D. and Angulo, J.M.: Spatio-temporal ltering using wavelets. Stoch. Environm. Res. Risk Assess. 16, 241-266 (2002).MATHCrossRefGoogle Scholar
  19. [18]
    Ruiz-Medina, M.D., Angulo, J.M. and Anh, V.V.: Fractional generalized random elds on bounded domains. Stoch. Anal. Appl. 21, 465-492 (2003).MATHCrossRefMathSciNetGoogle Scholar
  20. [19]
    Ruiz-Medina, , M.D., Angulo, J.M. and Fernández-Pascual, R.: Wavelet-vaguelette decomposition of spatiotemporal random elds. Stoch. Environm. Res. Risk Assess. 21,273-281 (2007).MATHCrossRefGoogle Scholar
  21. [20]
    Ramsay, J.O. and Silverman, B.W.: Functional data analysis. Springer. (2005).Google Scholar
  22. [21]
    Shumway, R.H.: Applied statistical time series analysis. Prentice-Hall. (1988).Google Scholar
  23. [22]
    Vidakovic, B.: Statistical modeling by wavelets. John Wiley & Sons. (1999).Google Scholar

Copyright information

© Physica-Verlag Heidelberg 2008

Authors and Affiliations

  • María Ruiz-Medina
    • 1
  1. 1.Department of Statistics and Operation ResearchsSpain

Personalised recommendations