论文标题
同时推断非SPARSE高维线性模型
Simultaneous Inference in Non-Sparse High-Dimensional Linear Models
论文作者
论文摘要
近年来，稀疏性假设下的推论和预测一直是一个热门的研究主题。但是，实际上，稀疏性假设很难测试，更重要的是通常会违反。在本文中，为了研究在非SPARSE高维线性模型下对任何一组参数的假设检验，我们将无效假设转换为可测试的力矩条件，然后使用自分裂结构在单样本和两样本病例下分别构建矩测试统计。与一个样本的情况相比，两个样本还需要卷积条件。值得注意的是，这些测试统计量包含修改后的Dantzig选择器，该统计数据同时估计模型参数和误差方差而没有稀疏假设。具体而言，我们的方法可以扩展到重型误差的稳健性。在非常温和的条件下，我们表明I型误差的概率渐近地等于名义水平α，II型误差的概率渐近为0。数值实验表明我们所提出的方法具有良好的有限样本性能。
Inference and prediction under the sparsity assumption have been a hot research topic in recent years. However, in practice, the sparsity assumption is difficult to test, and more importantly can usually be violated. In this paper, to study hypothesis test of any group of parameters under non-sparse high-dimensional linear models, we transform the null hypothesis to a testable moment condition and then use the self-normalization structure to construct moment test statistics under one-sample and two-sample cases, respectively. Compared to the one-sample case, the two-sample additionally requires a convolution condition. It is worth noticing that these test statistics contain Modified Dantzig Selector, which simultaneously estimates model parameters and error variance without sparse assumption. Specifically, our method can be extended to heavy tailed distributions of error for its robustness. On very mild conditions, we show that the probability of Type I error is asymptotically equal to the nominal level α and the probability of Type II error is asymptotically 0. Numerical experiments indicate that our proposed method has good finite-sample performance.
