Principal components analysis for sparsely observed correlated functional data using a kernel smoothing approach
| dc.creator | Paul, Debashis | |
| dc.creator | Peng, Jie | |
| dc.date | 2008-07-07 | |
| dc.date.accessioned | 2026-07-07T09:48:59Z | |
| dc.date.available | 2026-07-07T09:48:59Z | |
| dc.description | In this paper, we consider the problem of estimating the covariance kernel and its eigenvalues and eigenfunctions from sparse, irregularly observed, noise corrupted and (possibly) correlated functional data. We present a method based on pre-smoothing of individual sample curves through an appropriate kernel. We show that the naive empirical covariance of the pre-smoothed sample curves gives highly biased estimator of the covariance kernel along its diagonal. We attend to this problem by estimating the diagonal and off-diagonal parts of the covariance kernel separately. We then present a practical and efficient method for choosing the bandwidth for the kernel by using an approximation to the leave-one-curve-out cross validation score. We prove that under standard regularity conditions on the covariance kernel and assuming i.i.d. samples, the risk of our estimator, under $L^2$ loss, achieves the optimal nonparametric rate when the number of measurements per curve is bounded. We also show that even when the sample curves are correlated in such a way that the noiseless data has a separable covariance structure, the proposed method is still consistent and we quantify the role of this correlation in the risk of the estimator. | |
| dc.description | 58 pages | |
| dc.identifier | https://arxiv.org/abs/0807.1106 | |
| dc.identifier | http://arxiv.org/abs/0807.1106 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164417 | |
| dc.subject | Methodology | |
| dc.subject | Statistics Theory | |
| dc.title | Principal components analysis for sparsely observed correlated functional data using a kernel smoothing approach | |
| dc.type | text |