Date: Thursday, 12 June 2025, at 12.30pm (CET)

Dual format: ESSEC Paris La Défense (CNIT), Room TBA
and via Zoom, please click here

Extreme-order regression quantiles suffer from inconsistency and non-normal asymptotic distributions due to data sparsity in the tails. Building on extreme value theory, we propose a novel regression estimator called reinforced quantile regression, which explicitly extrapolates the score functions of quantile regression by incorporating power-law behavior for heavy-tailed outcomes or exponential transformations for light-tailed outcomes. We establish the asymptotic normality of this estimator, which converges at a rate strictly faster than that of classical quantile regression at extreme quantile levels. Furthermore, we have proved the asymptotic validity of bootstrap inference using random weights. Simulation results show that our estimator outperforms existing methods, offering more accurate estimation and narrower, near-exact bootstrap confidence intervals. Applying the proposed method to a dataset on Chinese twins, we find significant positive marginal predictive effects of education on upper-income percentiles. Unlike classical approaches, which show diminishing or even negative effects in the tails, our method yields stable and significantly positive estimates even at high quantile levels.

Kind regards,
Jeremy Heng, Olga Klopp, Roberto Reno, Marie Kratz and Riada Djebbar (Singapore Actuarial Society - ERM)