A Test for Jumps in Metric-Space Conditional Means
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908447072583680 |
|---|---|
| author | Van Dijcke, David |
| author_facet | Van Dijcke, David |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04560 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Test for Jumps in Metric-Space Conditional Means Van Dijcke, David Methodology Econometrics Statistics Theory 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. |
| title | A Test for Jumps in Metric-Space Conditional Means |
| topic | Methodology Econometrics Statistics Theory |
| url | https://arxiv.org/abs/2507.04560 |