Journal
TECHNOMETRICS
Volume 59, Issue 4, Pages 426-436Publisher
AMER STATISTICAL ASSOC
DOI: 10.1080/00401706.2016.1272495
Keywords
Dimension reduction; Multidimensional array; Neuroimaging analysis; Partial least squares; Reduced rank regression; Sparsity principle
Categories
Funding
- NSF [DMS-1613154, CCF-1617691, DMS-1310319, DMS-1613137]
- Division of Computing and Communication Foundations [1617691] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [1645093] Funding Source: National Science Foundation
Ask authors/readers for more resources
Partial least squares (PLS) is a prominent solution for dimension reduction and high-dimensional regressions. Recent prevalence of multidimensional tensor data has led to several tensor versions of the PLS algorithms. However, none offers a population model and interpretation, and statistical properties of the associated parameters remain intractable. In this article, we first propose a new tensor partial least-squares algorithm, then establish the corresponding population interpretation. This population investigation allows us to gain new insight on how the PLS achieves effective dimension reduction, to build connection with the notion of sufficient dimension reduction, and to obtain the asymptotic consistency of the PLS estimator. We compare our method, both analytically and numerically, with some alternative solutions. We also illustrate the efficacy of the new method on simulations and two neuroimaging data analyses. Supplementary materials for this article are available online.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available