Estimator Augmentation with Applications in High-Dimensional Group Inference

Understand

To make inference about a group of parameters on high-dimensional data, we develop the method of estimator augmentation for the block Lasso, which is defined via the block norm.

• By augmenting a block Lasso estimator $\hat{\beta}$ with the subgradient $S$ of the block norm evaluated at $\hat{\beta}$, we derive a closed-form density for the joint distribution of $(\hat{\beta},S)$ under a high-dimensional setting.
• This allows us to draw from an estimated sampling distribution of $\hat{\beta}$, or more generally any function of $(\hat{\beta},S)$, by Monte Carlo algorithms.
• We demonstrate the application of estimator augmentation in group inference with the group Lasso and a de-biased group Lasso constructed as a function of $(\hat{\beta},S)$.