Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/31148
Authors: 
Eilers, Paul H. C.
Heim, Susanne
Marx, Brian D.
Year of Publication: 
2005
Series/Report no.: 
Discussion paper // Sonderforschungsbereich 386 der Ludwig-Maximilians-Universität München 436
Abstract: 
We revisit a multidimensional varying-coefficient model (VCM), by allowing regressor coefficients to vary smoothly in more than one dimension, thereby extending the VCM of Hastie and Tibshirani. The motivating example is 3-dimensional, involving a special type of nuclear magnetic resonance measurement technique that is being used to estimate the diffusion tensor at each point in the human brain. We aim to improve the current state of the art, which is to apply a multiple regression model for each voxel separately using information from six or more volume images. We present a model, based on P-spline tensor products, to introduce spatial smoothness of the estimated diffusion tensor. Since the regression design matrix is space-invariant, a 4-dimensional tensor product model results, allowing more efficient computation with penalized array regression.
Subjects: 
Brain imaging
P-splines
Varying coefficient model
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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