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高维多任务回归问题的置信区间

Confidence intervals for high-dimensional multi-task regression

  • 摘要: 多元响应变量和预测变量之间的回归问题目前已被广泛应用于生物医学和经济学等领域。本文主要研究高维多任务学习问题中未知系数矩阵的统计推断问题。基于两步投影技术,我们按行构建了统计量。该方法通过消除重要信号的影响提高了推断效率。此外,通过建立该方法的渐近正态性,我们为未知系数矩阵的所有元素生成了相应的置信区间。最后,模拟研究和实际数据分析都验证了该方法的有效性。

     

    Abstract: Regression problems among multiple responses and predictors have been widely employed in many applications, such as biomedical sciences and economics. In this paper, we focus on statistical inference for the unknown coefficient matrix in high-dimensional multi-task learning problems. The new statistic is constructed in a row-wise manner based on a two-step projection technique, which improves the inference efficiency by removing the impacts of important signals. Based on the established asymptotic normality for the proposed two-step projection estimator (TPE), we generate corresponding confidence intervals for all components of the unknown coefficient matrix. The performance of the proposed method is presented through simulation studies and a real data analysis.

     

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