We consider statistical inference for errors-in-variables regression models with dependent observations under the high dimensionality of the error covariance matrix. It is tempting to prewhiten the model and data that had led to efficient weighted least squares estimation in the presence of the measurement errors, as being practised in the optimal fingerprinting approach in climate change studies. However, it is unclear to what extent the prewhitened estimator can improve the estimation efficiency of the unprewhitened estimator for errors-in-variables regression. We compare the prewhitening and unprewhitening estimators in terms of their estimation efficiency and computational cost. It shows that while the prewhitening operation does not necessarily improve the estimation efficiency of its unprewhitening counterpart, it demands more on the ensemble size needed in the error-covariance matrix estimation to ensure the asymptotic normality, and hence it would requires much more computationally resource.

翻译：本文考虑在误差协方差矩阵高维情形下，针对具有相依观测的变量误差回归模型进行统计推断。当存在测量误差时，对模型和数据进行预白化处理可导向高效的加权最小二乘估计，这一方法已在气候变化研究中的最优指纹技术中得到应用。然而，对于变量误差回归而言，预白化估计量能在多大程度上提升非预白化估计量的估计效率尚不明确。本文从估计效率与计算成本两个维度比较了预白化与非预白化估计量。研究表明：预白化操作未必能提升其对应非预白化估计量的估计效率，且为保证渐近正态性，该操作对误差协方差矩阵估计所需的集成规模提出更高要求，因而需要消耗更显著的计算资源。