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Automatic bias correction for testing in high-dimensional linear models
Statistica Neerlandica ( IF 1.5 ) Pub Date : 2022-07-01 , DOI: 10.1111/stan.12274
Jing Zhou 1 , Gerda Claeskens 1
Affiliation  

Hypothesis testing is challenging due to the test statistic's complicated asymptotic distribution when it is based on a regularized estimator in high dimensions. We propose a robust testing framework for 1$$ {\ell}_1 $$-regularized M-estimators to cope with non-Gaussian distributed regression errors, using the robust approximate message passing algorithm. The proposed framework enjoys an automatically built-in bias correction and is applicable with general convex nondifferentiable loss functions which also allows inference when the focus is a conditional quantile instead of the mean of the response. The estimator compares numerically well with the debiased and desparsified approaches while using the least squares loss function. The use of the Huber loss function demonstrates that the proposed construction provides stable confidence intervals under different regression error distributions.

中文翻译:

用于高维线性模型测试的自动偏差校正

当假设检验基于高维正则化估计量时,由于检验统计量的复杂渐近分布,因此假设检验具有挑战性。我们提出了一个强大的测试框架1个$$ {\ell}_1 $$-使用稳健的近似消息传递算法对正则化 M 估计器进行处理,以应对非高斯分布回归误差。所提出的框架享有自动内置的偏差校正,适用于一般的凸不可微损失函数,当焦点是条件分位数而不是响应的均值时,它也允许推断。在使用最小二乘损失函数时,估计器在数值上与去偏和去稀疏方法进行了很好的比较。Huber 损失函数的使用表明,所提出的构造在不同的回归误差分布下提供了稳定的置信区间。
更新日期:2022-07-01
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