Projection-based Inference for High-dimensional Linear Models
Projection-based Inference for High-dimensional Linear Models
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DOI：
10.5705/ss.202019.0283
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
S. Yi;Xianyang Zhang
中科院分区：
文献类型：
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作者：
S. Yi;Xianyang Zhang
我们提出了一种估计无偏Lasso估计中投影方向的新方法。其基本思想是将总体偏差分解为分别对应于强信号和弱信号的两个项。我们建议通过平衡与强信号和弱信号相关的平方偏差以及基于投影的估计器的方差来估计投影方向。标准的二次规划求解器可以有效地解决由此产生的优化问题。在理论上，我们证明了在适当的假设下，未知强信号集可以被一致估计，并且基于投影的估计器具有渐近正态。对我们的程序稍作修改，就会得到一个估计值，与原来的无偏套索相比，估计值的偏差可能会更小。我们进一步将我们的方法推广到对回归系数的稀疏线性组合进行推断。数值实验表明，该方法在覆盖精度方面优于已有的一些方法。
We develop a new method to estimate the projection direction in the debiased Lasso estimator. The basic idea is to decompose the overall bias into two terms corresponding to strong and weak signals respectively. We propose to estimate the projection direction by balancing the squared biases associated with the strong and weak signals as well as the variance of the projection-based estimator. Standard quadratic programming solver can efficiently solve the resulting optimization problem. In theory, we show that the unknown set of strong signals can be consistently estimated and the projection-based estimator enjoys the asymptotic normality under suitable assumptions. A slight modification of our procedure leads to an estimator with a potentially smaller order of bias comparing to the original debiased Lasso. We further generalize our method to conduct inference for a sparse linear combination of the regression coefficients. Numerical studies demonstrate the advantage of the proposed approach concerning coverage accuracy over some existing alternatives.