Conditional estimation for dependent functional data

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Title: Conditional estimation for dependent functional data
Authors: Battey, H
Sancetta, A
Item Type: Journal Article
Abstract: Suppose we observe a Markov chain taking values in a functional space. We are interested in exploiting the time series dependence in these infinite dimensional data in order to make non-trivial predictions about the future. Making use of the Karhunen–Loève (KL) representation of functional random variables in terms of the eigenfunctions of the covariance operator, we present a deliberately over-simplified nonparametric model, which allows us to achieve dimensionality reduction by considering one dimensional nearest neighbour (NN) estimators for the transition distribution of the random coefficients of the KL expansion. Under regularity conditions, we show that the NN estimator is consistent even when the coefficients of the KL expansion are estimated from the observations. This also allows us to deduce the consistency of conditional regression function estimators for functional data. We show via simulations and two empirical examples that the proposed NN estimator outperforms the state of the art when data are generated both by the functional autoregressive (FAR) model of Bosq (2000) [8] and by more general data generating mechanisms.
Issue Date: 26-Apr-2013
Date of Acceptance: 2-Aug-2012
ISSN: 0047-259X
Publisher: Elsevier
Start Page: 1
End Page: 17
Journal / Book Title: Journal of Multivariate Analysis
Volume: 120
Copyright Statement: © 2013 Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Keywords: Statistics & Probability
0104 Statistics
Publication Status: Published
Appears in Collections:Mathematics

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