论文标题
零估计方法，用于在高维无模型设置中估算信号水平
A zero-estimator approach for estimating the signal level in a high-dimensional model-free setting
论文作者
论文摘要
我们在假设已知的协变量分布的假设下研究了高维回归设置。我们旨在通过协变量的最佳线性函数（信号水平）估算响应中解释的差异。在我们的环境中，系数矢量的稀疏性或协变量的正态性或条件期望的线性性均未假定。我们提出了一个无偏见且一致的估计器，然后使用零估计器方法来改进它，其中零估计器是一个统计量，其期望值为零。 更普遍地，我们提出了一种基于零估计器方法的算法，原则上可以改善任何给定的估计器。我们研究了所提出的估计量的一些渐近特性，并在一项模拟研究中证明了它们的有限样本性能。
We study a high-dimensional regression setting under the assumption of known covariate distribution. We aim at estimating the amount of explained variation in the response by the best linear function of the covariates (the signal level). In our setting, neither sparsity of the coefficient vector, nor normality of the covariates or linearity of the conditional expectation are assumed. We present an unbiased and consistent estimator and then improve it by using a zero-estimator approach, where a zero-estimator is a statistic whose expected value is zero. More generally, we present an algorithm based on the zero estimator approach that in principle can improve any given estimator. We study some asymptotic properties of the proposed estimators and demonstrate their finite sample performance in a simulation study.
