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Weak convergence in the functional autoregressive model

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  • Mas, André
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    Abstract

    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 98 (2007)
    Issue (Month): 6 (July)
    Pages: 1231-1261

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    Handle: RePEc:eee:jmvana:v:98:y:2007:i:6:p:1231-1261

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    Related research

    Keywords: Functional data Autoregressive model Hilbert space Weak convergence Random operator Perturbation theory Linear inverse problem Martingale difference arrays;

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    Cited by:
    1. A. Berlinet & A. Elamine & A. Mas, 2011. "Local linear regression for functional data," Annals of the Institute of Statistical Mathematics, Springer, vol. 63(5), pages 1047-1075, October.
    2. A. Soltani & M. Hashemi, 2011. "Periodically correlated autoregressive Hilbertian processes," Statistical Inference for Stochastic Processes, Springer, vol. 14(2), pages 177-188, May.
    3. Esdras Joseph & Pedro Galeano & Rosa E. Lillo, 2013. "The Mahalanobis distance for functional data with applications to classification," Statistics and Econometrics Working Papers ws131312, Universidad Carlos III, Departamento de Estadística y Econometría.
    4. Park, Joon Y. & Qian, Junhui, 2012. "Functional regression of continuous state distributions," Journal of Econometrics, Elsevier, vol. 167(2), pages 397-412.

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