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Smoothed tensor quantile regression estimation for longitudinal data

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  • Ke, Baofang
  • Zhao, Weihua
  • Wang, Lei

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.

Suggested Citation

  • Ke, Baofang & Zhao, Weihua & Wang, Lei, 2023. "Smoothed tensor quantile regression estimation for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:csdana:v:178:y:2023:i:c:s016794732200189x
    DOI: 10.1016/j.csda.2022.107609
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    References listed on IDEAS

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