A1204
Title: Estimation of Tucker tensor factor models for high-dimensional higher-order tensor observations
Authors: Xu Zhang - South China Normal University (China) [presenting]
Abstract: Higher-order tensor data prevail in a wide range of fields, including finance and economics, high-resolution videos, multimodality imaging, engineering such as signal processing, and elsewhere. Tucker decomposition may be the most general low-rank approximation method among versatile decompositions of higher-order tensors owing to its strong compression ability, whilst statistical properties of the induced Tucker tensor factor model (TuTFaM) remains a big challenge and yet critical before it provides justification for applications in machine learning and beyond. Existing theoretical developments mainly focus on the field of time series with the assumption of strong auto-correlation among temporally ordered observations, which is ineffective for weakly dependent and independent tensor observations. Under quite mild assumptions, this article kicks off the participation of raw weakly correlated tensor observations within the TuTFaM setting. It proposes two sets of PCA-based estimation procedures, moPCA and its refinement IPmoPCA, the latter of which is enhanced in the rate of convergence. Their asymptotic behaviours, which can reduce to those in low-order tensor factor models in the existing literature, are developed. The proposed approaches outperform existing auto-covariance-based methods for tensor time series in terms of estimation and tensor reconstruction effects in both simulation experiments and two real data examples.
