Confidence Intervals and Regions for the Lasso by Using Stochastic Variational Inequality Techniques in Optimization
针对Lasso等稀疏正则化方法缺乏有效统计推断的问题，利用优化中的随机变分不等式技术，提出构建置信区间和置信域的方法，并通过模拟和实际数据验证其性能。
Summary Sparse regression techniques have been popular in recent years because of their ability in handling high dimensional data with built-in variable selection. The lasso is perhaps one of the most well-known examples. Despite intensive work in this direction, how to provide valid inference for sparse regularized methods remains a challenging statistical problem. We take a unique point of view of this problem and propose to make use of stochastic variational inequality techniques in optimization to derive confidence intervals and regions for the lasso. Some theoretical properties of the procedure are obtained. Both simulated and real data examples are used to demonstrate the performance of the method.