发表机构
Guanghua School of Management, Peking University（北京大学光华管理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对条件分位数约束识别的参数，提出自适应ℓ1惩罚上确界统计量及统一推断框架，含方差修正和自助法，模拟显示良好尺寸和功效。
AI 中文摘要
许多结构性和动态经济模型意味着关键参数由条件分位数约束识别。基于Bierens (1990)的指数加权方法和Chen等人 (2025)在条件矩约束的惩罚最大统计量方面的最新进展，我们为这类参数开发了一个统一的推断框架。我们提出了一个自适应ℓ1惩罚上确界统计量，该统计量将条件约束转化为连续统的无条件矩条件，并跨分位数指数聚合证据。该惩罚对加权方向上的最大化进行正则化。在所述的均匀性条件下，已知参数的自适应选择器不比未惩罚检验具有更低的最大最小局部功效，并且当某个正候选惩罚具有比零惩罚严格更大的总体最大最小准则时，产生严格的最大最小局部功效增益。我们将理论扩展到具有预估计 nuisance 参数的设置，刻画了插入步骤在极限过程中引起的额外项。我们推导了一个解析修正的方差估计器，该估计器考虑了插入估计的不确定性，并在原假设和局部备择序列下建立了高斯乘子自助法的有效性。蒙特卡洛模拟表明，所提出的CvM-KS聚合方案在线性设计中预估计下的拒绝率相对接近名义水平，并且在非线性设计中随着样本量的增长趋近名义水平。自适应和未惩罚程序之间的报告功效比较是特定于设计的，自适应程序沿某些方向具有更高的经验拒绝频率。
英文摘要
Many structural and dynamic economic models imply that key parameters are identified by conditional quantile restrictions. Building on the exponential-weighting approach of Bierens (1990) and recent advances in penalized maximum statistics for conditional moment restrictions (Chen et al., 2025), we develop a unified inference framework for such parameters. We propose an adaptive $\ell_1$-penalized supremum statistic that transforms the conditional restriction into a continuum of unconditional moment conditions and aggregates evidence across quantile indices. The penalty regularizes the maximization over the weighting direction. Under the stated uniformity conditions, the known-parameter adaptive selector has no lower maximin local power than the unpenalized test and yields a strict maximin local-power gain whenever some positive candidate penalty has a strictly larger population maximin criterion than the zero penalty. We extend the theory to settings with pre-estimated nuisance parameters, characterizing the additional terms induced by the plug-in step in the limiting process. We derive an analytically corrected variance estimator that accounts for plug-in estimation uncertainty and establish the validity of a Gaussian multiplier bootstrap under the null and sequences of local alternatives. Monte Carlo simulations show that the proposed CvM-KS aggregation scheme has rejection rates relatively close to nominal size under pre-estimation in the linear design and approaches the nominal level in nonlinear designs as the sample size grows. The reported power comparisons between the adaptive and unpenalized procedures are design-specific, with higher empirical rejection frequencies for the adaptive procedure along some directions.
Comments107 pages, 6 figures, 4 tables; includes the Supplementary Appendix
