Shrinkage methods are frequently used to estimate fixed effects to reduce the noisiness of the least square estimators. However, widely used shrinkage estimators guarantee such noise reduction only under strong distributional assumptions. I develop an estimator for the fixed effects that obtains the best possible mean squared error within a class of shrinkage estimators. This class includes conventional shrinkage estimators and the optimality does not require distributional assumptions. The estimator has an intuitive form and is easy to implement. Moreover, the fixed effects are allowed to vary with time and to be serially correlated, and the shrinkage optimally incorporates the underlying correlation structure in this case. In such a context, I also provide a method to forecast fixed effects one period ahead.

翻译：收缩方法通常用于估计固定效应，以降低最小二乘估计量的噪声。然而，广泛使用的收缩估计量仅在强分布假设下才能保证这种降噪效果。本文提出了一种固定效应的估计量，能在某一类收缩估计量中实现最优均方误差。该类估计量包含传统收缩估计量，且最优性不依赖分布假设。该估计量形式直观且易于实现。此外，固定效应允许随时间变化且存在序列相关性，此时收缩方法能最优地纳入潜在的相关结构。在此背景下，本文还提供了一种向前一期预测固定效应的方法。