Thomas T. Yang
arXiv 14 Oct 2026 · Econometrics
arXiv:2610.21019 · PDF · Extracted main text
We propose a test of whether the tail index of a heavy-tailed outcome is homogeneous across observed covariates. The key observation is that, under tail-index homogeneity, normalized log exceedances are asymptotically independent of the covariates even when tail frequencies vary with them. This leads to a simple-to-implement permutation test based on distance covariance, without estimating conditional tail indices or specifying the form of tail-index heterogeneity. For the global and locally balanced versions, we establish validity for order-statistic thresholds and give conditions for consistency and local power. Local balancing selects extremes within two covariate groups and can improve power when tail selection concentrates the covariates. Simulations illustrate these gains. In French motor insurance data, upper conditional quantiles vary with risk characteristics, but the tail-index tests do not reject a common tail index.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Székely, Gábor J. and Rizzo, Maria L. and Bakirov, Nail K (2007) Measuring and Testing Dependence by Correlation of Distances | 0.794 | 6 | 5 | 50% |
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| 3 | Chernozhukov, Victor (2005) Extremal Quantile Regression | 0.644 | 2 | 2 | 100% |
| 4 | Kinsvater, Paul and Fried, Roland (2017) Conditional Heavy-Tail Behavior with Applications to Precipitation and River Flow Extremes | 0.644 | 2 | 2 | 100% |
| 5 | Wang, Huixia Judy and Li, Deyuan and He, Xuming (2012) Estimation of High Conditional Quantiles for Heavy-Tailed Distributions | 0.644 | 2 | 2 | 100% |
| 6 | de Haan, Laurens and Zhou, Chen (2021) Trends in Extreme Value Indices | 0.644 | 2 | 2 | 100% |
| 7 | Yang, Thomas T (2026) On the Rank Condition of Tail Index Regressions and a Comparative Study with Extremal Quantile Regression self | 0.511 | 4 | 2 | 25% |
| 8 | Canay, Ivan A. and Kamat, Vishal (2018) Approximate Permutation Tests and Induced Order Statistics in the Regression Discontinuity Design | 0.405 | 1 | 1 | 100% |
| 9 | Canay, Ivan A. and Romano, Joseph P. and Shaikh, Azeem M (2017) Randomization Tests Under an Approximate Symmetry Assumption | 0.405 | 1 | 1 | 100% |
| 10 | Chen, Liujun and Zhou, Chen (2026) High-Dimensional Inference for Extreme Value Indices | 0.405 | 1 | 1 | 100% |
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