面向方差异质性的气候变化检测与归因的非线性收缩自适应指纹法
Adaptable Fingerprinting with Nonlinear Shrinkage for Climate Change Detection and Attribution under Variance Heterogeneity
AI总结：
该研究针对气候变化检测归因的高维场景，提出非线性收缩自适应指纹法，联合估计缩放与变异性膨胀因子，提升估计精度与置信区间性能，在气温数据应用中获更优归因结果。
AI中文摘要：
气候变化的检测与归因依赖于指纹法——一种线性变量误差回归框架，其中预测变量和响应变量均呈现由比例协方差结构控制的内部变异性，且受变异性膨胀因子约束。准确估计缩放因子（回归系数）依赖于从有限气候模型控制运行中推断回归误差的精度矩阵。在高维场景下，现有方法常忽略预测变量的方差膨胀，且存在精度矩阵估计不精确的问题，导致估计量有偏、不确定性被低估、置信区间覆盖率不佳。我们提出一种非线性、旋转不变的收缩框架用于估计精度矩阵，该框架可在高维场景下恢复总最小二乘估计量的渐近最优性。我们的方法联合估计缩放因子和变异性膨胀因子，从而校正估计偏差，并纳入一致方差估计量以实现有效的不确定性量化。我们还开发了残差一致性检验以评估模型充分性。数值研究表明该方法估计精确、置信区间覆盖率提升且效率更高。将其应用于1951-2020年的年平均近地表气温数据时，该方法生成更窄且更可靠的置信区间，得到更精细的归因结果。
英文摘要：
Detection and attribution of climate change relies on fingerprinting--a linear errors-in-variables regression framework in which both predictors and responses exhibit internal variability governed by a proportional covariance structure, subject to a variability inflation factor. Accurate estimation of the scaling factors (regression coefficients) depends on inferring the precision matrix of the regression errors from limited climate model control runs. In high-dimensional settings, existing approaches often overlook the variance inflation of the predictors and suffer from imprecise precision matrix estimates, yielding biased estimators, underestimated uncertainties, and confidence intervals with poor coverage. We propose a nonlinear, rotation-invariant shrinkage framework for estimating the precision matrix that restores the asymptotic optimality of the total least squares estimator in high-dimensional regimes. Our procedure jointly estimates the scaling factors and the variability inflation factor, thereby correcting estimation bias, and incorporates consistent variance estimators to enable valid uncertainty quantification. We also develop a residual consistency test to assess model adequacy. Numerical studies demonstrate precise estimation, improved confidence interval coverage, and higher efficiency. Applied to annual mean near-surface air temperature data from 1951--2020, our method produces narrower and more reliable confidence intervals, yielding refined attribution results.
