Empirical research typically involves a robustness-efficiency tradeoff. A researcher seeking to estimate a scalar parameter can invoke strong assumptions to motivate a restricted estimator that is precise but may be heavily biased, or they can relax some of these assumptions to motivate a more robust, but variable, unrestricted estimator. When a bound on the bias of the restricted estimator is available, it is optimal to shrink the unrestricted estimator towards the restricted estimator. For settings where a bound on the bias of the restricted estimator is unknown, we propose adaptive shrinkage estimators that minimize the percentage increase in worst case risk relative to an oracle that knows the bound. We show that adaptive estimators solve a weighted convex minimax problem and provide lookup tables facilitating their rapid computation. Revisiting five empirical studies where questions of model specification arise, we examine the advantages of adapting to -- rather than testing for -- misspecification.

翻译：实证研究通常涉及稳健性与效率的权衡。研究人员在估计标量参数时，可以借助强假设来驱动一个有约束的估计量，该估计量精确但可能存在严重偏差，或者他们可以放松部分假设，以驱动一个更稳健但变异性更大的无约束估计量。当有约束估计量的偏差边界已知时，将无约束估计量向有约束估计量收缩是最优的。针对有约束估计量偏差边界未知的情形，我们提出了自适应收缩估计量，该估计量最小化相对于知晓边界的理想情况的最坏情况风险百分比增长。我们证明自适应估计量解决了一个加权凸极小化问题，并提供了便于快速计算的查找表。通过重新审视五个涉及模型设定问题的实证研究，我们考察了适应（而非检验）错误设定的优势。