Asymptotic properties of bridge estimators in sparse high-dimensional regression models
稀疏高维回归模型中桥估计量的渐近性质AI 解读 ↓
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稀疏高维回归模型中桥估计量的渐近性质
- 研究问题
- 当线性回归的协变量数量随样本量增加时，桥估计能否一致识别非零系数，并使其估计达到已知零系数时的渐近表现？
- 方法与思路
- 作者分析稀疏高维线性模型中的桥估计，并在部分正交条件下研究边际桥估计，以处理协变量数超过样本量的筛选问题。
- 材料陈述的贡献
- 摘要称适当条件下桥估计具有变量选择一致性与预言性质；部分正交条件下，边际桥估计在维数超过样本量时仍可一致筛选。
- 阅读关注点
- 应区分完整桥估计的预言性质与边际桥估计的筛选结论，核对维数增长、惩罚设置及部分正交条件的具体要求。
- 阅读边界
- 依据 OpenAlex 索引摘要，稿件版本未注明；摘要未给出具体条件，也未声称维数超过样本量时完整桥估计仍有预言性质。
原文摘要
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.