Dabo-Niang, S;
Guillas, S;
Ternynck, C;
(2016)
Efficiency in multivariate functional nonparametric models with autoregressive errors.
Journal of Multivariate Analysis
, 147
pp. 168-182.
10.1016/j.jmva.2016.01.007.
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Abstract
In this paper, we introduce a new procedure for the estimation in the nonlinear functional regression model where the explanatory variable takes values in an abstract function space and the residual process is autocorrelated. Moreover, we consider the case where the response variable takes its values in Rd. The procedure consists in a pre-whitening transformation of the dependent variable based on the estimated autocorrelation. We establish both consistency and asymptotic normality of the regression function estimate. For kernel methods encountered in the literature, the correlation structure is commonly ignored (the so-called “working independence estimator”); we show here that there is a strong benefit in taking into account the autocorrelation in the error process. We also find that the improvement in efficiency can be large in our functional setting, up to 25% in the presence of high autocorrelation levels. We observe that the additional step of iterating the fitting process actually deteriorates the estimation. We illustrate the skills of the methods on simulations as well as on application on ozone levels over the US.
| Type: | Article |
|---|---|
| Title: | Efficiency in multivariate functional nonparametric models with autoregressive errors |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.jmva.2016.01.007 |
| Publisher version: | http://dx.doi.org/10.1016/j.jmva.2016.01.007 |
| Language: | English |
| Additional information: | Copyright © 2016. This manuscript version is published under a Creative Commons Attribution Non-commercial Non-derivative 4.0 International licence (CC BY-NC-ND 4.0). This licence allows you to share, copy, distribute and transmit the work for personal and non-commercial use providing author and publisher attribution is clearly stated. Further details about CC BY licences are available at http://creativecommons.org/licenses/by/4.0. |
| Keywords: | Autoregressive process; Functional data; Kernel regression; Pre-whitening; Time series |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1495949 |
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