Penalized partially linear models using orthonormal wavelet bases with an application to FMRI time series

Jalal M. Fadili (1) , E. T. Bullmore (2)

1 Equipe Image - Laboratoire GREYC - UMR6072
2 CAM - University of Cambridge [UK]

In this paper, we consider modeling the non-parametric component in partially linear models (PLM) using orthogonal wavelet expansions. We introduce a regularized estimator of the non-parametric part in the wavelet domain. The key innovation here is that the non-parametric part can be efficiently estimated by choosing an appropriate penalty function for which the hard and soft thresholding estimators are particular cases. This avoids excessive bias in estimating the parametric component. We give an efficient estimation algorithm. A large scale simulation study is also conducted to illustrate the finite sample properties of the estimator. The estimator is finally applied to real neurophysiological functional MRI data sets that are suspected to contain both smooth and transient drift features.

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Traitement des images [eess.IV]

Jalal M. Fadili, E. T. Bullmore. Penalized partially linear models using orthonormal wavelet bases with an application to FMRI time series. IEEE International symposium on biomedical imaging, 2004, Arlington, United States. pp.1171-1174, ⟨10.1109/ISBI.2004.1398752⟩. ⟨hal-00263558⟩