Weak convergence in the functional autoregressive model
The functional autoregressive model is a Markov model taylored for data of functional nature. It revealed fruitful when attempting to model samples of dependent random curves and has been widely studied along the past few years. This article aims at completing the theoretical study of the model by addressing the issue of weak convergence for estimates from the model. The main difficulties stem from an underlying inverse problem as well as from dependence between the data. Traditional facts about weak convergence in non-parametric models appear: the normalizing sequence is not an , a bias term appears. Several original features of the functional framework are pointed out.
Volume (Year): 98 (2007)
Issue (Month): 6 (July)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Philippe C. Besse, 2000. "Autoregressive Forecasting of Some Functional Climatic Variations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 673-687.
- Mas, André & Menneteau, Ludovic, 2003. "Large and moderate deviations for infinite-dimensional autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 241-260, November.
- André Mas, 1999. "Normalité asymptotique de l’estimateur empirique de l’opérateur d’autocorrélation d’un processus ARH(1)," Working Papers 99-11, Centre de Recherche en Economie et Statistique.
- Antoniadis, Anestis & Sapatinas, Theofanis, 2003. "Wavelet methods for continuous-time prediction using Hilbert-valued autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 133-158, October.
- Menneteau, Ludovic, 2005. "Some laws of the iterated logarithm in Hilbertian autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 405-425, February.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:98:y:2007:i:6:p:1231-1261. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If references are entirely missing, you can add them using this form.