论文标题
在稀疏测试的最小值指数上
On Minimax Exponents of Sparse Testing
论文作者
论文摘要
在高维线性回归的背景下，我们考虑了对稀疏替代方案进行全球测试的最小值风险的确切渐近剂。我们的结果表征了该最小值风险在几个制度中的领先顺序行为，从而发现了其行为的新相位过渡。这补充了在此问题中表征渐近一致性的大量文献，并提供了有用的基准，可以将特定测试的性能进行比较。最后，我们提供了一些初步证据，表明流行的稀疏性自适应程序在最小风险方面可能是最佳的。
We consider exact asymptotics of the minimax risk for global testing against sparse alternatives in the context of high dimensional linear regression. Our results characterize the leading order behavior of this minimax risk in several regimes, uncovering new phase transitions in its behavior. This complements a vast literature characterizing asymptotic consistency in this problem, and provides a useful benchmark, against which the performance of specific tests may be compared. Finally, we provide some preliminary evidence that popular sparsity adaptive procedures might be sub-optimal in terms of the minimax risk.
