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英文文献：Stein-Rule Estimation and Generalized Shrinkage Methods for Forecasting Using Many Predictors-Stein-Rule估计和广义收缩方法用于使用许多预测器的预测
英文文献作者：Eric Hillebrand,Tae-Hwy Lee
英文文献摘要：
We examine the Stein-rule shrinkage estimator for possible improvements in estimation and forecasting when there are many predictors in a linear time series model. We consider the Stein-rule estimator of Hill and Judge (1987) that shrinks the unrestricted unbiased OLS estimator towards a restricted biased principal component (PC) estimator. Since the Stein-rule estimator combines the OLS and PC estimators, it is a model-averaging estimator and produces a combined forecast. The conditions under which the improvement can be achieved depend on several unknown parameters that determine the degree of the Stein-rule shrinkage. We conduct Monte Carlo simulations to examine these parameter regions. The overall picture that emerges is that the Stein-rule shrinkage estimator can dominate both OLS and principal components estimators within an intermediate range of the signal-to-noise ratio. If the signal-to-noise ratio is low, the PC estimator is superior. If the signal-to-noise ratio is high, the OLS estimator is superior. In out-of-sample forecasting with AR(1) predictors, the Stein-rule shrinkage estimator can dominate both OLS and PC estimators when the predictors exhibit low persistence.

当线性时间序列模型中有许多预测因子时，我们检查斯坦因规则收缩估计器，以改进估计和预测。我们考虑Hill和Judge(1987)的Stein-rule估计量，它将无限制无偏OLS估计量压缩成一个有限制有偏主成分估计量。由于Stein-rule估计器结合了OLS估计器和PC估计器，它是一种模型平均估计器并产生组合预测。改善的条件取决于几个未知的参数，这些参数决定了斯坦氏收缩的程度。我们进行蒙特卡罗模拟来检查这些参数区域。在信噪比的中间范围内，斯坦规则收缩估计器可以控制OLS估计器和主成分估计器。如果信噪比较低，PC估计器是优越的。当信噪比较高时，OLS估计具有优越性。在使用AR(1)预测器进行样本外预测时，当预测器表现出低持久性时，施泰因规则收缩估计器可以同时支配OLS和PC估计器。

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