Conditional estimation for dependent functional data

Heather Battey and Alessio Sancetta

Journal of Multivariate Analysis, 2013, vol. 120, issue C, 1-17

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.

Keywords: Functional data analysis; Karhunen–Loève expansion; Dimension reduction; Nearest neighbour estimator (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047259X13000638
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:120:y:2013:i:c:p:1-17

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.jmva.2013.04.009

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().