  High-dimensional tensor-valued data have recently gained attention from
researchers in economics and finance. We consider the estimation and inference
of high-dimensional tensor factor models, where each dimension of the tensor
diverges. Our focus is on a factor model that admits CP-type tensor
decomposition, which allows for non-orthogonal loading vectors. Based on the
contemporary covariance matrix, we propose an iterative simultaneous projection
estimation method. Our estimator is robust to weak dependence among factors and
weak correlation across different dimensions in the idiosyncratic shocks. We
establish an inferential theory, demonstrating both consistency and asymptotic
normality under relaxed assumptions. Within a unified framework, we consider
two eigenvalue ratio-based estimators for the number of factors in a tensor
factor model and justify their consistency. Through a simulation study and two
empirical applications featuring sorted portfolios and international trade
flows, we illustrate the advantages of our proposed estimator over existing
methodologies in the literature.
