Work

Mean Dimension Reduction And Testing For Nonparametric Tensor Response Regression

Year: 2023

Type: article

Abstract: In this article, we propose a flexible model-free approach to the regression analysis of a tensor response and a vector predictor.Without specifying the specific form of the regression mean function, we consider two closely related statistical problems: (i) estimation of the dimension reduction subspace that captures all the variations in the regression mean function, and (ii) hypothesis testing of whether the conditional expectation of a linear dimension reduction of the response given the predictor is invariant to the changes in the predictor.We propose a new nonparametric metric called tensor martingale difference divergence, and study its statistical properties.Built on this new metric, we develop computationally efficient estimation and asymptotically valid testing procedures.We demonstrate the efficacy of our method through both simulations and two real data applications for macroeconomics and e-commerce.

Source: Statistica Sinica

DOI: 10.5705/ss.202022.0075

Authors: Chung Eun Lee, Xin Zhang, Lexin Li

Institutions: Florida State University, Baruch College, University of California, Berkeley

Language: English

Topic: Tensor decomposition and applications

Subfield: Computational Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, National Institutes of Health, National Institute on Aging

Awards: Collaborative Research: New Regression Models and Methods for Studying Multiple Categorical Responses, New Statistical Methods for Multicenter Multimodal Longitudinal Neuroimaging Analysis, Tensor and Subspace Learning Methods with Applications to Medical Imaging, Mechanisms of Alzheimer's Disease Progression in the Aging Brain, CIF: Small: Collaborative Research: Graphical Modeling of Multivariate Functional Data