Uniform Inference for Parameters Identified by Conditional Quantile Restrictions

2026-09-19

AI Summary

本文针对由条件分位数限制识别的关键参数，提出了一种自适应ℓ1-惩罚的统计方法，并构建了一个统一的推断框架。

Abstract

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.

Problem

• Conditional Quantile Restrictions
• Uniform Inference
• Economic Models

Innovation

• adaptive $\ell_1$-penalized supremum statistic
• conditional quantile restrictions
• Gaussian multiplier bootstrap
• uniform inference