On Nonparametric Feature Filters in Electromagnetic Imaging

Estimation of sparse time-varying coefficients on the basis of time-dependent observations is one of the most challenging problems in statistics. Our study was mainly motivated

from magnetoencephalographic neuroimaging, where we want to

identify neural activities using the magnetoencephalographic sensor measurements outside the brain. The problem is ill-posed since the observed magnetic field could result from an infinite number of possible neuronal sources. The so-called minimum-variance beamformer is one of data-adaptive nonparametric feature filters to address the above problem in the literature. In this paper, we propose a method of sure feature filtering for a high-dimensional time-varying coefficient model. The new method assumes that the correlation structure of the sensor measurements can be well represented by a set of non-orthogonal

variance-covariance components. We develop a theory on the sure screening property of the proposed filters and on when the beamformer-based location estimators are consistent or inconsistent with the true ones. We also derive the lower and upper bounds for the mean filtering errors of the proposed method. The new theory is further supported by simulations and a real data analysis.