Tensor Principal Component Analysis
39 Pages Posted: 4 Jan 2023 Last revised: 14 Apr 2023
Date Written: December 25, 2022
In this paper, we develop new methods for analyzing high-dimensional tensor datasets. A tensor factor model describes a high-dimensional dataset as a sum of a low-rank component and an idiosyncratic noise, generalizing traditional factor models for panel data. We propose an estimation algorithm, called tensor principal component analysis (PCA), which generalizes the traditional PCA applicable to panel data. The algorithm involves unfolding the tensor into a sequence of matrices along different dimensions and applying PCA to the unfolded matrices. We provide theoretical results on the consistency and asymptotic distribution for tensor PCA estimator of loadings and factors. The algorithm demonstrates good performance in Mote Carlo experiments and is applied to sorted portfolios.
Keywords: Principal component analysis, tensor data, singular value and canonical polyadic decompositions
JEL Classification: C10, C33, C38, C55
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