DC-TNN decomposes tensors into low-rank core plus sparse refinement fed to coupled neural channels, yielding non-asymptotic risk bounds and the first distribution-free conformal procedure for selecting among tensor decompositions.
Helping Effects Against Curse of Dimensionality in Threshold Factor Models for Matrix Time Series
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abstract
As is known, factor analysis is a popular method to reduce dimension for high-dimensional data. For matrix data, the dimension reduction can be more effectively achieved through both row and column directions. In this paper, we introduce a threshold factor models to analyze matrix-valued high-dimensional time series data. The factor loadings are allowed to switch between regimes, controlling by a threshold variable. The estimation methods for loading spaces, threshold value, and the number of factors are proposed. The asymptotic properties of these estimators are investigated. Not only the strengths of thresholding and factors, but also their interactions from different directions and different regimes play an important role on the estimation performance. When the thresholding and factors are all strong across regimes, the estimation is immune to the impact that the increase of dimension brings, which breaks the curse of dimensionality. When the thresholding in two directions and factors across regimes have different levels of strength, we show that estimators for loadings and threshold value experience 'helping' effects against the curse of dimensionality. We also discover that even when the numbers of factors are overestimated, the estimators are still consistent. The proposed methods are illustrated with both simulated and real examples.
verdicts
UNVERDICTED 2representative citing papers
Develops consistent estimators for pre- and post-change factor loadings and change-point location in high-dimensional time series allowing strong cross-sectional noise dependence through self-normalized testing.
citing papers explorer
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Dual-Channel Tensor Neural Networks: Finite-Sample Theory and Conformal Structure Selection
DC-TNN decomposes tensors into low-rank core plus sparse refinement fed to coupled neural channels, yielding non-asymptotic risk bounds and the first distribution-free conformal procedure for selecting among tensor decompositions.
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Factor Analysis for High-Dimensional Time Series with Change Point
Develops consistent estimators for pre- and post-change factor loadings and change-point location in high-dimensional time series allowing strong cross-sectional noise dependence through self-normalized testing.