Functional nonparametric model for time series: a fractal approach for dimension reduction

Vieu, Philippe; Ferraty, Frédéric; Goia, Aldo

doi:10.1007/bf02595710

Cited by 72 publications

(42 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…By combining the above bounds T 0,N , T 1,N and T 2,N , summing over i ∈ I in T 0,N and over i 1 , i 2 ∈ I in T 1,N and T 2,N , and using (10), we arrive at (8), thus completing the proof. …”

Section: Accepted M Manuscriptmentioning

confidence: 69%

Bandwidth selection for functional time series prediction

Antoniadis

Paparoditis

Sapatinas

2009

Statistics & Probability Letters

View full text Add to dashboard Cite

We propose a method to select the bandwidth for functional time series prediction. The idea underlying this method is to calculate the empirical risk of prediction using past segments of the observed series and to select as value of the bandwidth for prediction the bandwidth which minimizes this risk. We prove an oracle bound for the proposed bandwidth estimator showing that it mimics, asymptotically, the value of the bandwidth which minimizes the unknown theoretical risk of prediction based on past segments. We illustrate the usefulness of the proposed estimator in finite sample situations by means of a small simulation study and compare the resulting predictions with those obtained by a leave-one-curve-out cross-validation estimator used in the literature.

show abstract

Section: Accepted M Manuscriptmentioning

confidence: 69%

Bandwidth selection for functional time series prediction

Antoniadis

Paparoditis

Sapatinas

2009

Statistics & Probability Letters

View full text Add to dashboard Cite

show abstract

“…The same thing is done, with more explicit details, along the proof of Lemma 4.5 in [2]. Precisely, as indicated on p. 339 of [2], the compact set is written in such a way that, for any l > 0,…”

Section: The New Topological Conditionmentioning

confidence: 99%

Erratum of: ‘Non-parametric models for functional data, with application in regression, time-series prediction and curve discrimination’

Ferraty

Vieu

2008

Journal of Nonparametric Statistics

View full text Add to dashboard Cite

“…On the other hand, more and more works deal with nonparametric approaches for variables valued in an infinite dimensional space. Gasser et al [6] proposed an estimate of the mode of a distribution of random curves whereas Ferraty et al [3] studied a kernel estimator in the functional regression setting. Note also that a kernel estimator for functional conditional distribution has been introduced by Ferraty et al [5].…”

Section: Introductionmentioning

confidence: 99%