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之间的权衡。研究人员在估计标量参数时，可以采用强假设来构建一个精确但可能严重有偏的受限估计量，或者放宽部分假设以构建一个更稳健但方差较大的无约束估计量。当受限估计量的偏差上界已知时，将无约束估计量向受限估计量收缩是最优策略。对于受限估计量偏差上界未知的情形，我们提出了自适应收缩估计量，该估计量能够最小化相对于知晓该上界的理想基准的最坏情况风险百分比增幅。我们证明自适应估计量可求解加权凸极小极大问题，并提供速查表以简化其快速计算。通过重新审视五个涉及模型设定问题的实证研究，我们分析了适应——而非检验——误设定的优势。