发表机构
Aarhus University; Hitotsubashi University; London School of Economics（奥胡斯大学; 一桥大学; 伦敦政治经济学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出交叉拟合方差估计框架，通过消除残差漂移提升二次型检验的功效，在设定、过度识别及多重约束检验中优于传统插入式估计，并在俄勒冈健康保险实验中验证。
AI 中文摘要
二次型检验统计量在计量经济学中被广泛使用，其性能取决于准确的方差估计。传统的插入式估计量在原假设下是一致的，但在备择假设下，残差中的漂移会使其膨胀，导致检验失去功效。我们为这类统计量中的方差估计开发了一个通用框架，将两个平方残差因子之一替换为残差的辅助线性组合（“交叉拟合”），该组合被选择用以消除漂移。我们精确刻画了每个估计量的条件偏差。漂移以平方形式进入插入式估计量，并乘以有界远离零的量，因此只要漂移非退化，其偏差即为正。漂移仅通过交叉拟合后存留的部分影响交叉拟合估计量，且仅通过残差生成矩阵的非对角元素产生影响。由此计算，我们得到了交叉拟合估计量在备择假设下保持一致而插入式估计量不一致的条件。在共同的临界值下，交叉拟合检验在插入式检验拒绝时也拒绝；面对遥远备择假设，插入式统计量收敛于有限极限，当携带偏离的观测很少时该极限很小：其功效可能趋于零，而交叉拟合检验的功效趋于一。我们在非参数设定检验、过度识别检验和多重线性约束检验的原初假设下验证了这些条件，并在俄勒冈健康保险实验中说明了该程序。
英文摘要
Quadratic-form test statistics are widely used in econometrics, and their performance depends on accurate variance estimation. Conventional plug-in estimators are consistent under the null hypothesis, but under alternatives the drift in the residuals inflates them and the test loses power. We develop a general framework for variance estimation in such statistics, replacing one of the two squared-residual factors by an auxiliary linear combination of the residuals (``cross-fitting'') chosen to annihilate the drift. We characterize the conditional bias of each estimator exactly. The drift enters the plug-in estimator squared, multiplied by quantities bounded away from zero, so its bias is positive whenever the drift is non-degenerate. It reaches the cross-fit estimator only through the part that survives the cross-fitting, and then only through off-diagonal entries of a residual-maker matrix. From this calculation we obtain conditions under which the cross-fit estimator remains consistent under alternatives while the plug-in estimator does not. At a common critical value the cross-fit test therefore rejects whenever the plug-in test does, and against distant alternatives the plug-in statistic converges to a finite limit, small when few observations carry the departure: its power can tend to zero where the cross-fit test's tends to one. We verify the conditions under primitive assumptions in nonparametric specification testing, overidentification testing, and testing many linear restrictions, and illustrate the procedure on the Oregon Health Insurance Experiment.
