Smoothed tensor quantile regression estimation for longitudinal data

Baofang Ke, Weihua Zhao and Lei Wang

Computational Statistics & Data Analysis, 2023, vol. 178, issue C

Abstract: As extensions of vector and matrix data with ultrahigh dimensionality and complex structures, tensor data are fast emerging in a large variety of scientific applications. In this paper, a two-stage estimation procedure for linear tensor quantile regression (QR) with longitudinal data is proposed. In the first stage, we account for within-subject correlations by using the generalized estimating equations and then impose a low-rank assumption on tensor coefficients to reduce the number of parameters by a canonical polyadic decomposition. To avoid the asymptotic analysis and computation problems caused by the non-smooth QR score function, kernel smoothing method is applied in the second stage to construct the smoothed tensor QR estimator. When the number of rank is given, a block-relaxation algorithm is proposed to estimate the regression coefficients. A modified BIC is applied to estimate the number of rank in practice and show the rank selection consistency. Further, a regularized estimator and its algorithm are investigated for better interpretation and efficiency. The asymptotic properties of the proposed estimators are established. Simulation studies and a real example on Beijing Air Quality data set are provided to show the performance of the proposed estimators.

Keywords: Generalized estimating equations; Longitudinal data; Quantile regression; Tensor regression; CP decomposition (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:178:y:2023:i:c:s016794732200189x

DOI: 10.1016/j.csda.2022.107609

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