The rate of convergence for sparse and low-rank quantile trace regression

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2023-06-19 DOI:10.1016/j.jco.2023.101778

Xiangyong Tan , Ling Peng , Peiwen Xiao , Qing Liu , Xiaohui Liu

引用次数: 0

Abstract

Trace regression models are widely used in applications involving panel data, images, genomic microarrays, etc., where high-dimensional covariates are often involved. However, the existing research involving high-dimensional covariates focuses mainly on the condition mean model. In this paper, we extend the trace regression model to the quantile trace regression model when the parameter is a matrix of simultaneously low rank and row (column) sparsity. The convergence rate of the penalized estimator is derived under mild conditions. Simulations, as well as a real data application, are also carried out for illustration.

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稀疏和低秩分位数迹回归的收敛速度

痕量回归模型广泛应用于面板数据、图像、基因组微阵列等涉及高维协变量的应用中。然而，现有的涉及高维协变量的研究主要集中在条件均值模型上。本文将跟踪回归模型推广到参数为低秩低列稀疏矩阵时的分位数跟踪回归模型。在温和条件下，导出了惩罚估计量的收敛速度。仿真和实际数据应用也进行了说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Complexity 工程技术-计算机：理论方法

CiteScore

3.10

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The multidisciplinary Journal of Complexity publishes original research papers that contain substantial mathematical results on complexity as broadly conceived. Outstanding review papers will also be published. In the area of computational complexity, the focus is on complexity over the reals, with the emphasis on lower bounds and optimal algorithms. The Journal of Complexity also publishes articles that provide major new algorithms or make important progress on upper bounds. Other models of computation, such as the Turing machine model, are also of interest. Computational complexity results in a wide variety of areas are solicited. Areas Include: • Approximation theory • Biomedical computing • Compressed computing and sensing • Computational finance • Computational number theory • Computational stochastics • Control theory • Cryptography • Design of experiments • Differential equations • Discrete problems • Distributed and parallel computation • High and infinite-dimensional problems • Information-based complexity • Inverse and ill-posed problems • Machine learning • Markov chain Monte Carlo • Monte Carlo and quasi-Monte Carlo • Multivariate integration and approximation • Noisy data • Nonlinear and algebraic equations • Numerical analysis • Operator equations • Optimization • Quantum computing • Scientific computation • Tractability of multivariate problems • Vision and image understanding.