Radchenko, Peter, Qiao, Xinghao 
ORCID: 0000-0002-6546-6595 and James, Gareth M.
(2015)
Index models for sparsely sampled functional data.
Journal of the American Statistical Association, 110 (510).
824 - 836.
ISSN 0162-1459
Abstract
The regression problem involving functional predictors has many important appli- cations and a number of functional regression methods have been developed. However, a common complication in functional data analysis is one of sparsely observed curves, that is predictors that are observed, with error, on a small subset of the possible time points. Such sparsely observed data induces an errors-in-variables model, where one must account for measurement error in the functional predictors. Faced with sparsely observed data, most current functional regression methods simply estimate the un- observed predictors and treat them as fully observed; thus failing to account for the extra uncertainty from the measurement error. We propose a new functional errors-in- variables approach, Sparse Index Model Functional Estimation (SIMFE), which uses a functional index model formulation to deal with sparsely observed predictors. SIMFE has several advantages over more traditional methods. First, the index model imple- ments a non-linear regression and uses an accurate supervised method to estimate the lower dimensional space into which the predictors should be projected. Second, SIMFE can be applied to both scalar and functional responses and multiple predictors. Finally, SIMFE uses a mixed effects model to effectively deal with very sparsely observed functional predictors and to correctly model the measurement error.
Actions (login required)
 |
View Item |
Download Statistics
Download Statistics