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：实证研究通常涉及鲁棒性与效率之间的权衡。研究者若要估计标量参数，可借助强假设构建受限估计量，该估计量精确但可能存在严重偏误；亦可放宽部分假设以构建更稳健但方差较大的无限制估计量。当受限估计量的偏误上界已知时，将无限制估计量向受限估计量收缩是最优策略。针对受限估计量偏误上界未知的情形，我们提出自适应收缩估计量，该估计量可将相对于知晓该上界的理想估计量的最坏情形风险百分比增量最小化。我们证明自适应估计量可求解加权凸极小化问题，并提供便于快速计算的查表工具。通过重新审视五个存在模型设定问题的实证研究，我们分析了适应而非检验误设的优势。