Estimation of Low Rank High-Dimensional Multivariate Linear Models for Multi-Response Data
Estimation of Low Rank High-Dimensional Multivariate Linear Models for Multi-Response Data
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DOI：
10.1080/01621459.2020.1799813
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发表时间：
2020-08
影响因子：
3.7
通讯作者：
Changliang Zou;Y. Ke;Wenyang Zhang
中科院分区：
文献类型：
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作者：
Changliang Zou;Y. Ke;Wenyang Zhang
摘要 在本文中，我们研究了高维多响应数据的低秩高维多元线性模型（LRMLM）。我们提出了一种直观有吸引力的估计方法，并开发了一种用于实现目的的算法。建立渐近性质是为了从理论上证明估计过程的合理性。还进行了深入的模拟研究，以证明样本量有限时的性能，并与文献中的一些流行方法进行比较。结果表明，所提出的估计器在各种情况下都优于所有替代方法。最后，使用我们建议的估计程序，我们应用 LRMLM 来分析环境数据集并预测相关位置的 PM2.5 浓度。结果说明了所提出的方法如何提供比其他方法更准确的预测。
Abstract In this article, we study low rank high-dimensional multivariate linear models (LRMLM) for high-dimensional multi-response data. We propose an intuitively appealing estimation approach and develop an algorithm for implementation purposes. Asymptotic properties are established to justify the estimation procedure theoretically. Intensive simulation studies are also conducted to demonstrate performance when the sample size is finite, and a comparison is made with some popular methods from the literature. The results show the proposed estimator outperforms all of the alternative methods under various circumstances. Finally, using our suggested estimation procedure we apply the LRMLM to analyze an environmental dataset and predict concentrations of PM2.5 at the locations concerned. The results illustrate how the proposed method provides more accurate predictions than the alternative approaches.