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• W3103117922 abstract "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." @default.
• W3103117922 created "2020-11-23" @default.
• W3103117922 creator A5032703090 @default.
• W3103117922 creator A5090717566 @default.
• W3103117922 date "2017-01-01" @default.
• W3103117922 modified "2023-09-24" @default.
• W3103117922 title "Adaptive higher-order spectral estimators" @default.
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• W3103117922 doi "https://doi.org/10.1214/17-ejs1330" @default.
• W3103117922 hasPublicationYear "2017" @default.
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