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Abstract:
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Sufficient dimension reduction methods are flexible tools for data visualization and exploratory analysis, typically in regression problems with a univariate response $Y$ and a multivariate predictor $\mbX$. In recent years, there has been a growing literature on the statistical analysis of tensor-variate data. When X is tensor-variate, Li, Kim and Altman (2010) proposed the general framework of ``dimension folding'' methods for reducing X without loss of information and several moment-based approaches. In this article, we propose likelihood-based dimension folding methods for reducing the tensor predictor more efficiently. Theoretically, we derive the maximum likelihood estimators under different scenarios; empirically, we show that the proposed methods are more accurate in simulations and real data analysis.
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