Honest Confidence Sets for Sparsely and Non-Sparsely Tuned Model Selection Estimators

在这个项目中，我们想要研究收缩估计的分布性质，例如流行的Lasso估计和其他正则化方法，目的是在这些估计的基础上得到诚实的置信度。这种估计器在最近的统计文献中引起了极大的兴趣。然而，如何基于这样的估计器构造有效的置信度集在很大程度上仍然是未知的-这是一个既具有理论意义又具有实际意义的问题。

In this project we want to investigate the distributional properties of shrinkage estimators, such as the popular Lasso estimator and other regularization methods, with the aim of deriving honest confidence sets based on the these estimators. This kind of estimators has seen immense interest in recent statistics literature. However, it is still largely unknown how to construct valid confidence sets based on such an estimator – a question that is both of theoretical as well as of practical interest.