基于权重矩阵优化尺度因子估计效率的气候变化检测与归因中的正则化指纹方法
Regularized Fingerprinting in Detection and Attribution of Climate Change with Weight Matrix Optimizing the Efficiency in Scaling Factor Estimation
AI总结：
本文提出用非线性收缩估计误差协方差矩阵构造权重矩阵，以优化气候变化检测与归因中尺度因子的估计效率，并在渐近和有限样本下验证其优于现有线性收缩方法。
摘要：
用于气候变化检测与归因的最优指纹方法基于多元回归，其中每个协变量具有测量误差，其协方差矩阵与回归误差的协方差矩阵相同，仅相差一个已知的尺度因子。关于回归系数的推断至关重要，不仅用于对检测与归因作出判断，也用于量化由检测与归因分析得到的重要结果的不确定性。当不存在变量误差（EIV）时，估计回归系数的最优权重矩阵是回归误差的精度矩阵，但在实践中该矩阵从未已知，必须从气候模式模拟中估计。我们通过求逆误差协方差矩阵的非线性收缩估计来构造权重矩阵，该估计直接最小化针对所得回归系数估计量不确定性的损失函数。所得回归系数估计量在气候模式模拟样本量和矩阵维度以有限比率共同趋于无穷时是渐近最优的。当存在变量误差时，基于所提权重矩阵的回归系数估计量比基于现有误差协方差矩阵线性收缩估计之逆的估计量渐近更有效。在模拟现实情形的有限样本模拟研究中，通过回归系数的置信区间长度和经验覆盖率验证了该方法的性能。对不同空间尺度平均温度进行检测与归因分析的应用说明了该方法的实用性。
英文摘要：
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.
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