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Tensor Principal Component Analysis

Andrii BabiiEric GhyselsJunsu Pan
Dec 2022
摘要
In this paper, we develop new methods for analyzing high-dimensional tensordatasets. A tensor factor model describes a high-dimensional dataset as a sumof a low-rank component and an idiosyncratic noise, generalizing traditionalfactor models for panel data. We propose an estimation algorithm, called tensorprincipal component analysis (PCA), which generalizes the traditional PCAapplicable to panel data. The algorithm involves unfolding the tensor into asequence of matrices along different dimensions and applying PCA to theunfolded matrices. We provide theoretical results on the consistency andasymptotic distribution for tensor PCA estimator of loadings and factors. Thealgorithm demonstrates good performance in Mote Carlo experiments and isapplied to sorted portfolios.
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