Power enhancement via cross-fit variance estimation: Applications to specification, overidentification, and many-restriction testing
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交叉拟合方差估计的功效增强：模型设定、过度识别与多重约束检验
- 研究问题
- 研究二次型检验在备择假设下为何因残差漂移导致方差高估与功效损失，以及如何改造方差估计以减轻这一问题。
- 方法与思路
- 作者以能消除漂移的残差辅助线性组合替换两个残差平方因子之一，精确分析条件偏差，并在三类检验中验证条件。
- 材料陈述的贡献
- 摘要称，在给定条件下交叉拟合方差在备择下仍一致；某些远端备择下，其功效可趋于一，而插件检验功效可趋于零。
- 阅读关注点
- 应核对辅助组合的构造、漂移消除与非对角项条件，以及共同临界值下拒绝关系的适用范围和有限样本校准。
- 阅读边界
- 这是 arXiv 预印本，不能据此声称已同行评审或期刊接收。摘要未提供完整条件或应用数值，功效结论不能理解为无条件支配。
原文摘要
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.