Rank-based score tests for high-dimensional regression coefficients
Rank-based score tests for high-dimensional regression coefficients
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DOI：
10.1214/13-ejs839
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发表时间：
2013
影响因子：
1.1
通讯作者：
Long Feng;Changliang Zou;Zhaojun Wang;Bin Chen
中科院分区：
文献类型：
--
作者：
Long Feng;Changliang Zou;Zhaojun Wang;Bin Chen
摘要：本文涉及高维设置中线性回归系数的同时测试。当维数大于样本量时，经典的 F 检验不适用，因为样本协方差矩阵不可逆。最近，[5]和[17]提出了通过排除 F 统计量中的逆项来进行测试的程序。然而，这种基于 F 统计量的方法的效率受到外围观测值和重尾分布的不利影响。为了克服这个问题，我们提出了一种基于排名回归的稳健评分测试。建立了高维零假设和替代假设下所提出的检验统计量的渐近分布。与 t 检验相比，其相对于 [17] 检验的渐近相对效率与 Wilcoxon 检验密切相关。进行模拟研究是为了将所提出的程序与其他现有测试程序进行比较，并表明我们的程序在规模和功效方面通常都更加稳健。
Abstract: This article is concerned with simultaneous tests on linear regression coefficients in high-dimensional settings. When the dimensionality is larger than the sample size, the classic F -test is not applicable since the sample covariance matrix is not invertible. Recently, [5] and [17] proposed testing procedures by excluding the inverse term in F -statistics. However, the efficiency of such F -statistic-based methods is adversely affected by outlying observations and heavy tailed distributions. To overcome this issue, we propose a robust score test based on rank regression. The asymptotic distributions of the proposed test statistic under the high-dimensional null and alternative hypotheses are established. Its asymptotic relative efficiency with respect to [17]’s test is closely related to that of the Wilcoxon test in comparison with the t-test. Simulation studies are conducted to compare the proposed procedure with other existing testing procedures and show that our procedure is generally more robust in both sizes and powers.