Weak convergence in the functional autoregressive model

By André Mas. 2005

64 citations recorded by the source corpus.

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 On, a bias term appears. Several original features of the functional framework are pointed out.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/53ff412a95f86558bd7e43d29dcc3cc9a11f381c

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Citations in the corpus

Local linear regression for functional data (2007, methodology): “The interested reader will find them in Mas (2007b).”
White Noise Testing and Model Diagnostic Checking for Functional Time Series (2016, unknown): “For h ≥ 2, |||γε,0ρh−1∗ γ −1 X πkT γX πkT γ −1 X ρ h−1γε,0|||1 ≤ ∥γε,0∥ 2 S∥γ −1/2 X ρ h−1 ∥ 2 L ∞ provided that ∥γ −1/2 X ρ∥L ∞ [also see Assumption A1 in Mas (2007).”
CLT in functional linear regression models (2005, background): “When assumption (A:3) holds, Cesaro’s mean Theorem ensures that the term on the left above tends to zero. We turn to the rst term in equation ( 26 ) 0”