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Abstract Observations in various applications are frequently represented as a time series of multidimensional arrays, called tensor time series, preserving the inherent multidimensional structure. In this paper, we present a factor model approach, in a form similar to tensor CANDECOMP/PARAFAC (CP) decomposition, to the analysis of high-dimensional dynamic tensor time series. As the loading vectors are uniquely defined but not necessarily orthogonal, it is significantly different from the existing tensor factor models based on Tucker-type tensor decomposition. The model structure allows for a set of uncorrelated one-dimensional latent dynamic factor processes, making it much more convenient to study the underlying dynamics of the time series. A new high-order projection estimator is proposed for such a factor model, utilizing the special structure and the idea of the higher order orthogonal iteration procedures commonly used in Tucker-type tensor factor model and general tensor CP decomposition procedures. Theoretical investigation provides statistical error bounds for the proposed methods, which shows the significant advantage of utilizing the special model structure. Simulation study is conducted to further demonstrate the finite sample properties of the estimators. Real data application is used to illustrate the model and its interpretations.
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Orthogonal Arrays: A Review
ABSTRACT Orthogonal arrays are arguably one of the most fascinating and important statistical tools for efficient data collection. They have a simple, natural definition, desirable properties when used as fractional factorials, and a rich and beautiful mathematical theory. Their connections with combinatorics, finite fields, geometry, and error‐correcting codes are profound. Orthogonal arrays have been widely used in agriculture, engineering, manufacturing, and high‐technology industries for quality and productivity improvement experiments. In recent years, they have drawn rapidly growing interest from various fields such as computer experiments, integration, visualization, optimization, big data, machine learning/artificial intelligence through successful applications in those fields. We review the fundamental concepts and statistical properties and report recent developments. Discussions of recent applications and connections with various fields are presented. Some interesting open research directions are also presented.
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- Award ID(s):
- 2304767
- PAR ID:
- 10593629
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- WIREs Computational Statistics
- Volume:
- 17
- Issue:
- 2
- ISSN:
- 1939-5108
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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