Abstract

Post-selection inference has been an active research topic recently. A lot of work provided different ways to solve practical problems in many fields such as medicine, finance, and so on. In particular, post-selection inference under the linear model is widely discussed. We extend it to generalized linear model and present new approaches for post-selection inference for penalized least squares method. The core of this framework is the distribution function of the post-selection estimation conditioned on the selection event. Then, lasso and elastic net are used to select models to construct the effective confidence interval of the selected coefficient. The theoretical results and the numerical comparisons show that our methods are better than the existing ones. Finally, the proposed methods are applied to the analysis of real data sets.

摘要

选择后推理最近一直是一个活跃的研究课题。许多工作为解决医学、金融等许多领域的实际问题提供了不同的途径。特别是，广泛讨论了线性模型下的选择后推理。我们将其扩展到广义线性模型，并提出了惩罚最小二乘法的选择后推理的新方法。该框架的核心是基于选择事件的选择后估计的分布函数。然后，使用 lasso 和弹性网络来选择模型，以构建所选系数的有效置信区间。理论结果和数值比较表明，我们的方法优于现有方法。最后，将所提出的方法应用于真实数据集的分析。