2025/07/06 by David Van Dijcke, Van Dijcke, David
Computer Science · #Advanced Multi-Objective Optimization Algorithms #Econometrics (econ.EM) #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2507.04560
openalex publication_date 2025/07/06 · openalex created_date 2025/10/20 · openalex updated_date 2026/07/28
Standard methods for detecting discontinuities in conditional means are not applicable to outcomes that are complex, non-Euclidean objects like distributions, networks, or covariance matrices. This article develops a nonparametric test for jumps in conditional means when outcomes lie in a non-Euclidean metric space. Using local Fréchet regression, the method estimates a mean path on either side of a candidate cutoff. This extends existing k-sample tests to a non-parametric regression setting with metric-space valued outcomes. I establish the asymptotic distribution of the test and its consistency against contiguous alternatives. For this, I derive a central limit theorem for the local estimator of the conditional Fréchet variance and a consistent estimator of its asymptotic variance. Simulations confirm nominal size control and robust power in finite samples. Two empirical illustrations demonstrate the method's ability to reveal discontinuities missed by scalar-based tests. I find sharp changes in (i) work-from-home compositions at an income threshold for non-compete enforceability and (ii) national input-output networks following the loss of preferential U.S. trade access. These findings show the value of analyzing regression outcomes in their native metric spaces.