Open Access
2017 Adaptive higher-order spectral estimators
David Gerard, Peter Hoff
Electron. J. Statist. 11(2): 3703-3737 (2017). DOI: 10.1214/17-EJS1330


Many applications involve estimation of a signal matrix from a noisy data matrix. In such cases, it has been observed that estimators that shrink or truncate the singular values of the data matrix perform well when the signal matrix has approximately low rank. In this article, we generalize this approach to the estimation of a tensor of parameters from noisy tensor data. We develop new classes of estimators that shrink or threshold the mode-specific singular values from the higher-order singular value decomposition. These classes of estimators are indexed by tuning parameters, which we adaptively choose from the data by minimizing Stein’s unbiased risk estimate. In particular, this procedure provides a way to estimate the multilinear rank of the underlying signal tensor. Using simulation studies under a variety of conditions, we show that our estimators perform well when the mean tensor has approximately low multilinear rank, and perform competitively when the signal tensor does not have approximately low multilinear rank. We illustrate the use of these methods in an application to multivariate relational data.


Download Citation

David Gerard. Peter Hoff. "Adaptive higher-order spectral estimators." Electron. J. Statist. 11 (2) 3703 - 3737, 2017.


Received: 1 February 2017; Published: 2017
First available in Project Euclid: 9 October 2017

zbMATH: 1373.62251
MathSciNet: MR3709867
Digital Object Identifier: 10.1214/17-EJS1330

Primary: 62H12
Secondary: 15A69 , 62C99 , 91D30

Keywords: Higher-order SVD , network , relational data , shrinkage , SURE , tensor

Vol.11 • No. 2 • 2017
Back to Top