Factor-driven completion of tensor data with missing entries

Abstract

This article proposes a novel method for tensor data completion based on a factor model and a slicing technique. Specifically, we first focus on third-order tensor data with missing values. Under the assumption of factor structure, the rows and columns of the matrix consisting of slices of each dimension are reordered. Then, we divide it into four blocks to obtain valid estimates of factors and factor loadings in different blocks. Finally, these estimates are utilized to complete the missing values. In addition, we extend our proposed method to address the issue of missing entries in higher-order tensors. The core idea is to slice the higher-order data into multiple two-dimensional matrix slices using recursive methods. To evaluate its effectiveness, we apply the method to third-order tensor simulation data and the Fama-French return series, which yields satisfactory results.