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量的分布性质，比如流行的Lasso估计量和其他正则化方法，目的是基于这些估计量推导可靠的置信集。这类估计器在最近的统计文献中引起了极大的兴趣。然而，如何在这样一个估计量的基础上构造有效的置信集仍然是一个很大程度上未知的问题，这既是一个理论问题，也是一个实际问题。

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.