Partial Quantile Tensor Regression

Dayu Sun, Limin Peng, Zhiping Qiu, Ying Guo and Amita Manatunga

Journal of the American Statistical Association, 2025, vol. 120, issue 551, 1724-1735

Abstract: Tensors, characterized as multidimensional arrays, are frequently encountered in modern scientific studies. Quantile regression has the unique capacity to explore how a tensor covariate influences different segments of the response distribution. In this work, we propose a partial quantile tensor regression (PQTR) framework, which novelly applies the core principle of the partial least squares technique to achieve effective dimension reduction for quantile regression with a tensor covariate. The proposed PQTR algorithm is computationally efficient and scalable to a large tensor covariate. Moreover, we uncover an appealing latent variable model representation for the PQTR algorithm, justifying a simple population interpretation of the resulting estimator. We further investigate the connection of the PQTR procedure with an envelope quantile tensor regression (EQTR) model, which defines a general set of sparsity conditions tailored to quantile tensor regression. We prove the root-n consistency of the PQTR estimator under the EQTR model, and demonstrate its superior finite-sample performance compared to benchmark methods through simulation studies. We demonstrate the practical utility of the proposed method via an application to a neuroimaging study of post traumatic stress disorder (PTSD). Results derived from the proposed method are more neurobiologically meaningful and interpretable as compared to those from existing methods. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Date: 2025
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DOI: 10.1080/01621459.2024.2422129

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