Xiong (2010)提出了线性回归模型基于Mallows准则的NG (nonnegative garrote) 估计量,但对该估计量的合理性尚未给出理论上的证明. 文章借鉴模型平均估计的渐近最优的思想, 分别构建了在方差已知与方差未知情形下的基于Mallows 准则的NG估计量的渐近最优的定理, 并给出了相应的证明, 为Xiong (2010) 提出的方法提供了理论支持.

Xiong (2010) proposed using Mallows criterion to obtain the nonnegative garrote (NG) estimator for linear regression model, but the rationality of the estimator has not been proved theoretically. In this paper, we refer to the idea of the asymptotic optimality of the model average estimator, and show the asymptotic optimality of NG estimator based on Mallows criterion in term of known variance and unknown variance, and provide theoretical support for the method proposed by Xiong (2010).