DIMENSION FOLDING PCA AND PFC FOR MATRIX- VALUED PREDICTORS

Conventional dimension reduction methods mainly deal with simple data structure and are inappropriate for data with matrix-valued predictors. Li et al. (2010) proposed dimension folding methods that eectively improve major moment- based dimension reduction techniques for the more complex data structure. Their methods, however, are moment-based and rely on slicing the responses to gain in- formation about the conditional distribution of XjY . This could be inadequate when the number of slices is not chosen properly. In this paper, we propose model- based dimension folding methods that can be treated as extensions of conventional principal components analysis (PCA) and principal tted components (PFC). We refer to them as dimension folding PCA and dimension folding PFC. The pro- posed methods can simultaneously reduce a predictor's multiple dimensions and inherit asymptotic properties from maximum likelihood estimation. Dimension folding PFC gains further eciency by eective use of the response information. Both methods can provide robust estimation and are computationally ecient. We