| Theory, methods and application of statistical analysis of large-p-small-n cross-correlation matrices arising in fMRI studies of neuroplasticity are discussed. It is proposed to conduct such an analysis based on a voxel-to-voxel level which immediately yields large cross-correlation matrices. Furthermore, the matrices have an interesting property to have both sparse and dense rows and columns. The theory is developed in a nonparametric regression setting. The main steps in solving the problem are: (i) treat observations, available for a single voxel, as a nonparametric regression; (ii) use a wavelet transform and then work with empirical wavelet coefficients; (iii) develop the theory and methods of adaptive simultaneous confidence intervals and adaptive rate-minimax thresholding estimation for the matrices. The developed methods are illustrated via analysis of fMRI experiments and the results allow us to not only conclude that during fMRI experiments there is a change in cross-correlation between left and right hemispheres (the fact well known in the literature), but that we can also enrich our understanding of how neural pathways are activated on a single voxel-to-voxel level. |
