Advertisement

TEST

, Volume 22, Issue 2, pp 224–226 | Cite as

Comments on: Model-free model-fitting and predictive distributions

  • Manuel Febrero–BandeEmail author
Discussion
  • 78 Downloads

Summary

This paper provides a new useful insight about the problem of constructing prediction intervals with the minimum number of assumptions including invoking any particular model on the data. The overall procedure is based on the model-free prediction principle, which relies on the idea of finding an invertible transformation H such that the data (response and explanatory variables) are mapped onto a i.i.d. vector with distribution Fn. Along Sect. 3, with detailed examples mainly devoted to nonparametric estimators, this idea is employed based on a model, i.e. the transformation H that converts the original data Yt and their covariates Xt into i.i.d. residuals and/or i.i.d. predictive residuals has a closed form chosen by the practitioner. Two methods are proposed in this section. The first one, based on fitted residuals, is called model-based (MB) whereas the second one, based on predictive residuals, is called model-free/model-based(MF/MB). In the paper, a resampling algorithm...

Keywords

Conditional Distribution Prediction Interval Predictive Distribution Nonparametric Estimator Functional Data Analysis 
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.

Notes

Acknowledgements

I would like to thank the editors of TEST for their invitation to comment on such an interesting paper. This research is partly supported by Grant MTM2008-03010.

References

  1. Ferraty F, Vieu P (2006) Nonparametric functional data analysis: theory and practice. Springer, Berlin zbMATHGoogle Scholar
  2. Ferraty F, Rabhi A, Vieu P (2005) Conditional quantiles for dependent functional data with application to the climatic “el niño” phenomenon. Sankhya 67(2):378–398 MathSciNetzbMATHGoogle Scholar
  3. Ferraty F, Laksaci A, Vieu P (2006) Estimating some characteristics of the conditional distribution in nonparametric functional models. Stat Inference Stoch Process 9(1):47–76 MathSciNetzbMATHCrossRefGoogle Scholar
  4. Ferraty F, Keilegom I, Vieu P (2010) On the validity of the bootstrap in non-parametric functional regression. Scand J Stat 37(2):286–306 MathSciNetzbMATHCrossRefGoogle Scholar
  5. Olive DJ (2007) Prediction intervals for regression models. Comput Stat Data Anal 51(6):3115–3122 MathSciNetzbMATHCrossRefGoogle Scholar
  6. Shi S (1991) Local bootstrap. Ann Inst Stat Math 43:667–676 zbMATHCrossRefGoogle Scholar
  7. Stine RA (1985) Bootstrap prediction intervals for regression. J Am Stat Assoc 80(392):1026–1031 MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Sociedad de Estadística e Investigación Operativa 2013

Authors and Affiliations

  1. 1.Department of Statistics and Operations Research, Faculty of MathematicsUniversity of Santiago de CompostelaSantiago de CompostelaSpain

Personalised recommendations