论文标题
通过重量矩阵优化缩放因子估计的效率，在检测和归因于气候变化的检测和归因方面的正则指纹识别
Regularized Fingerprinting in Detection and Attribution of Climate Change with Weight Matrix Optimizing the Efficiency in Scaling Factor Estimation
论文作者
论文摘要
气候变化检测和归因的最佳指纹方法是基于多元回归的，在该方法中，每个协方差都有测量误差，其协方差矩阵与回归误差的协方差矩阵相同，直至已知的量表。关于回归系数的推论不仅对于发表有关检测和归因的陈述至关重要，而且对于量化了从检测和归因分析得出的重要结果中的不确定性。当没有变异的错误（EIV）时，估计回归系数的最佳权重矩阵是回归误差的精确矩阵，在实践中，它永远不会知道，并且必须从气候模型模拟中估算。我们通过反转误差协方差矩阵的非线性收缩估计来构建权重矩阵，该误差协方差矩阵将损耗函数最小化，直接针对所得的回归系数估计器的不确定性。回归系数的最终估计量在气候模型模拟的样本量和矩阵尺寸与限制比率的情况下渐近最佳。当存在EIV时，基于提出的权重矩阵的回归系数的估计器比基于现有的误差协方差矩阵的现有线性收缩估计器的倒数更有效。该方法的性能在有限样本模拟研究中得到了证实，该研究以置信区间的长度和回归系数的经验覆盖率来模仿现实情况。在不同空间尺度下平均温度检测和归因分析的应用说明了该方法的效用。
The optimal fingerprinting method for detection and attribution of climate change is based on a multiple regression where each covariate has measurement error whose covariance matrix is the same as that of the regression error up to a known scale. Inferences about the regression coefficients are critical not only for making statements about detection and attribution but also for quantifying the uncertainty in important outcomes derived from detection and attribution analyses. When there is no errors-in-variables (EIV), the optimal weight matrix in estimating the regression coefficients is the precision matrix of the regression error which, in practice, is never known and has to be estimated from climate model simulations. We construct a weight matrix by inverting a nonlinear shrinkage estimate of the error covariance matrix that minimizes loss functions directly targeting the uncertainty of the resulting regression coefficient estimator. The resulting estimator of the regression coefficients is asymptotically optimal as the sample size of the climate model simulations and the matrix dimension go to infinity together with a limiting ratio. When EIVs are present, the estimator of the regression coefficients based on the proposed weight matrix is asymptotically more efficient than that based on the inverse of the existing linear shrinkage estimator of the error covariance matrix. The performance of the method is confirmed in finite sample simulation studies mimicking realistic situations in terms of the length of the confidence intervals and empirical coverage rates for the regression coefficients. An application to detection and attribution analyses of the mean temperature at different spatial scales illustrates the utility of the method.
