强相关数据回归
Regression with strongly correlated data
摘要：
本文讨论了强相关数据的线性回归，例如，在磁流体动力学平衡重建。我们证明了，一般地，对于固定的样本量，当相关性变为1时，估计的回归参数的协方差阵趋于零。也就是说，在这个极限中，估计参数以完美的精度已知。简单的例子来说明这种效果和特殊情况下，估计协方差不为零的性质。
英文摘要：
This paper discusses linear regression of strongly correlated data that arises, for example, in magnetohydrodynamic equilibrium reconstructions. We have proved that, generically, the covariance matrix of the estimated regression parameters for fixed sample size goes to zero as the correlations become unity. That is, in this limit the estimated parameters are known with perfect accuracy. Simple examples are shown to illustrate this effect and the nature of the exceptional cases in which the estimate covariance does not go to zero.
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