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Xiao-Jun Song

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Preprint Oct 2026

Tuning-Free Tests for Treatment Effect Heterogeneity via Expectile Processes

This paper develops tuning-free tests for treatment-effect heterogeneity. By characterizing the null hypothesis as constancy of the expectile treatment-effect curve, we construct test statistics as continuous functionals of the mean-centered sample expectile process. We establish a uniform Bahadur representation, deriv...

Hao Lu, Xiao-Jun Song · 0 citations
Preprint Oct 2026

Testing Treatment Effect Heterogeneity with Functional Outcomes

Assessing treatment-effect heterogeneity is important in causal inference, particularly for functional outcomes where effects may vary over time and the common effect is unknown. We propose a nonparametric procedure that assesses treatment-effect homogeneity through a testable marginal implication. By comparing within-...

Yong-Zhen Feng, Jie Li, Xiao-Jun Song · 0 citations
Preprint Sep 2026

Uniform Inference for Parameters Identified by Conditional Quantile Restrictions

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 in...

Xu-Qing Lin, Xiao-Jun Song · 0 citations
Preprint Sep 2026

Testing Conditional Stochastic Dominance via Copula Derivatives

Comparing two populations at the same physical covariate value requires more than conditional means or isolated target-point decisions: researchers may need evidence about an entire conditional-distribution ordering over a continuum, even when covariate margins differ. This paper makes that common-value comparison esti...

Wei-Qi Yang, Wei-Wei Zhuang, Xiao-Jun Song · 0 citations
Review Jul 2026

Kernel Minimum Distance Estimation and Testing with Conditional Moment Restrictions: A Unified Framework

We propose a unified Kernel Minimum Distance (KMD) framework for estimating and testing models defined by conditional moment restrictions. By embedding conditional moments into a Reproducing Kernel Hilbert Space (RKHS), we construct a closed-form $V$-statistic objective function that quantifies the distance from the re...

Yu-Hao Li, Hao Lu, Xiao-Jun Song · 0 citations
Preprint Jul 2026

Orthogonal Integrated Conditional Moment Tests for Treatment Effect Heterogeneity

We propose a nonparametric integrated conditional moment (ICM) test for treatment effect heterogeneity across subpopulations defined by a given covariate subvector. Under unconfoundedness, the null is recast as a conditional moment restriction based on a Neyman-orthogonal score, which reduces the first-order sensitivit...

Hao Lu, Xiao-Jun Song · 0 citations

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