标题： 稀疏高维回归模型中桥估计量的渐近性质 显示英文标题

标题： Asymptotic properties of bridge estimators in sparse high-dimensional regression models

摘要： 我们研究了稀疏、高维、线性回归模型中桥估计量的渐近性质，其中协变量的数量可能随样本量趋于无穷大。 我们特别感兴趣的是使用桥估计量来区分系数为零的协变量和系数非零的协变量。 我们证明，在适当的条件下，桥估计量以收敛到1的概率正确选择具有非零系数的协变量，并且非零系数估计量的渐近分布与它们在事先知道零系数的情况下所具有的分布相同。 因此，桥估计量具有Fan和Li [J. Amer. Statist. Assoc. 96 (2001) 1348--1360]以及Fan和Peng [Ann. Statist. 32 (2004) 928--961]定义的“oracle”性质。 一般情况下，只有当协变量的数量小于样本量时，“oracle”性质才成立。 然而，在零系数协变量与非零系数协变量不相关或弱相关的部分正交性条件下，我们证明即使协变量的数量大于样本量，边缘桥估计量也能以收敛到1的概率正确区分非零系数和零系数的协变量。 显示英文摘要

摘要： We study the asymptotic properties of bridge estimators in sparse, high-dimensional, linear regression models when the number of covariates may increase to infinity with the sample size. We are particularly interested in the use of bridge estimators to distinguish between covariates whose coefficients are zero and covariates whose coefficients are nonzero. We show that under appropriate conditions, bridge estimators correctly select covariates with nonzero coefficients with probability converging to one and that the estimators of nonzero coefficients have the same asymptotic distribution that they would have if the zero coefficients were known in advance. Thus, bridge estimators have an oracle property in the sense of Fan and Li [J. Amer. Statist. Assoc. 96 (2001) 1348--1360] and Fan and Peng [Ann. Statist. 32 (2004) 928--961]. In general, the oracle property holds only if the number of covariates is smaller than the sample size. However, under a partial orthogonality condition in which the covariates of the zero coefficients are uncorrelated or weakly correlated with the covariates of nonzero coefficients, we show that marginal bridge estimators can correctly distinguish between covariates with nonzero and zero coefficients with probability converging to one even when the number of covariates is greater than the sample size.