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High-dimensional Inference in Magnetoencephalographic Neuroimaging

Banff International Research Station for Mathematical Innovation and Discovery

Estimation of a high-dimensional time-varying coefficient model on the basis of spatially correlated observations is one of challenging problems in statistics. Our study was motivated by source localization problem in magnetoencephalographic (MEG) neuroimaging, where we want to identify neural activities using MEG 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. In this paper, we propose a family of methods for coefficient screening by using sensor covariance thresholding and shrinkage. The new methods assume that the structure of sensor measurements can be modelled by a set of non-orthogonal covariance components. We develop an asymptotic theory for identifying non-zero coefficients estimators. We also derive the lower and upper bounds for the mean screening errors of the proposed methods under certain conditions. The new theory is further illustrated by simulations and a real data analysis.

Mathematics; Statistics; Biology and other natural sciences; Applied statistics

video/mp4

Author affiliation: University of Kent

2014-08-07

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/49837

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/