标题： 稀疏线性回归中$l_2$范数的估计和未知方差的检验 显示英文标题

标题： Estimation of the $l_2$-norm and testing in sparse linear regression with unknown variance

摘要： 我们考虑在未知方差的稀疏线性回归中估计$l_2$-范数和平方$l_2$-范数的相关问题，以及在具有$l_2$分离的稀疏替代假设下检验回归参数为零的假设问题。我们在这三个问题中建立了最小最大最优估计（分别地，检验）速率。 显示英文摘要

摘要： We consider the related problems of estimating the $l_2$-norm and the squared $l_2$-norm in sparse linear regression with unknown variance, as well as the problem of testing the hypothesis that the regression parameter is null under sparse alternatives with $l_2$ separation. We establish the minimax optimal rates of estimation (respectively, testing) in these three problems.